To show that any matrix of rank r can be written as the sum of r matrices of rank 1, we will use the concept of matrix decomposition.
Let's consider an arbitrary matrix A of size m x n with rank r. By definition, the rank of a matrix is the maximum number of linearly independent rows or columns. This means that we can express A as a sum of r matrices of rank 1.
We start by performing the singular value decomposition (SVD) of matrix A:
A = U * Σ * V^T
where U is an m x r matrix, Σ is an r x r diagonal matrix with non-negative singular values on the diagonal, and V^T is the transpose of an r x n matrix V.
We can rewrite the singular value decomposition as:
A = σ1 * u1 * v1^T + σ2 * u2 * v2^T + ... + σr * ur * vr^T
where σ1, σ2, ..., σr are the singular values of A, and u1, u2, ..., ur and v1, v2, ..., vr are the corresponding left and right singular vectors, respectively.
Each term in the above expression is a rank 1 matrix, as it is an outer product of a column vector and a row vector. The rank 1 matrices are of the form x * y^T, where x and y are column vectors.
Thus, we have expressed matrix A as the sum of r matrices of rank 1.
In summary, any matrix of rank r can be written as the sum of r matrices of rank 1, where each term in the sum is a rank 1 matrix obtained from the singular value decomposition of the original matrix.
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If a single 2 hp motor draws 13.8 amps on 115 volt ac current, how much current would 9 identical motors pull?
what is the answer and how do you solve it?
The current drawn by 9 identical motors will be 124.2 amps current
Current is the flow of electrical charge carriers like electrons. Current flows from negative to positive points. The SI unit for measuring electric current is the ampere (A). One ampere of current is defined as one coulomb of electrical charge moving past a unique point in a second.
since , one motor of 2hp draws = 13.8 amps current
hence , 9 identical motor will pull = 13.8 * 9 (each will pull same amount of current )
= 124.2 amps current
The current drawn by 9 identical motors will be 124.2 amps current
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Solve the equation: -8(2a-1)=36
-8.(2a - 1) = 36
-16a + 8 = 36
-16a = 36 - 8 = 28
a = 28/(-16) = -7/4
The correct answer is -7/4 = -1.75
The solution to the given equation is [tex]\frac{-7}{4}[/tex].
What is an expression?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.
We have,
Expression -8(2a - 1) = 36
So,
Now,
To get the solution to this expression,
i.e.
-8(2a - 1) = 36
Rewrite it as,
i.e.
Opening Brackets,
We get,
-16a + 8 = 36
Now,
Taking variable terms on one side and other terms on another side,
We get,
-16a = 36 - 8
On solving we get,
-16a = 28
i.e.
a = [tex]\frac{-28}{16} = \frac{-7}{4}[/tex]
So,
The solution to the given equation is [tex]\frac{-7}{4}[/tex].
Hence, we can say that the solution to the given equation is [tex]\frac{-7}{4}[/tex].
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If you place a 39-foot ladder against the top of a building and the bottom of the
ladder is 33 feet from the bottom of the building, how tall is the building? Round to
the nearest tenth of a foot.
Answer:
20.8
Step-by-step explanation:
Just use the The Pythagorean Theorem
which is a^2+b^2=c^2
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Pls, I need help. Whoever gets it right gets the brainliest.
There can be 18, 12, 9, 6, 4 , 3 or 2 students on each team depending on the number of teams selected.
How to know the number of students on each team?Considering there are at least 2 teams but no more than 19 teams, let's calculate the number of students in each case:
2 teams: 18 students per team (36/2 = 18)3 teams: 12 students per team (36/3 =12)4 teams: 9 students per team (36/4 = 9)6 teams: 6 students per team (36/6 = 6)9 teams: 4 students per team (36/9 = 4)12 teams: 3 students per team (36/12= 3)18 teams: 2 students per team (36/18 = 2)Learn more about teams in: https://brainly.com/question/10750297
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How can a right triangular cross-section be created from a right triangle ?
Answer:
in a triangle prism each cross section parallel to the triangular base is a triangle congruent to the base
The point-slope form of the
equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = ~(x - 8). What is
the slope-intercept form of the
equation for this line?
y= ~x-12
y= =x-4
y=~x+2
V= x+6
Answer: y = -x + 2
Step-by-step explanation:
Point slope form is y - y = m(x - x)
m = the slope of the line
Slope-intercept form is y = mx + b
m = the slope of the line
b = y-intercept
So because the - is in the m spot in the point-slope form, that means that is the slope of the line meaning it will also be in the m spot in slope-intercept form. The y-intercept of the line is found when x is 0. When we look at the two coordinates provided you can see that one of them shows when x is 0. We see that when x is 0, y is 2 which means that the y-intercept is 2.
So when you put the 2 in place of b, you get y = -x + 2
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. the patient currently has a bone density of 1, 500 kg / m * g ^ 3 the doctor writes an exponential function to represent the situation. which should the doctor use for a and b in a function written in the form f(x) = a * b ^ x where f(x) represents the bone density after x years ?
Answer:
a = 1500 b = .97
Step-by-step explanation:
1500 ( .97)^x = bone density after n years
3% loss leave 97% each year (.97 in decimal)
1. A circle has a radius of 12 in. Find:
The diameter of the circle.
The circumference of the circle.
The area of the circle.
2. A circle has a radius of 4.4 cm. Find:
The diameter of the circle.
The circumference of the circle.
The area of the circle.
3. A circle has a diameter of 60 m. Find:
The radius of the circle.
The circumference of the circle.
The area of the circle.
4. A circle has a diameter of 1.8 km. Find:
The radius of the circle.
The circumference of the circle.
The area of the circle.
Answer:
1.
a.) 24in
b.)75.36in
c.)452.16in
Step-by-step explanation:
1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.
1b. the circumfrence of a circle is C (Circumfrence)=[tex]2\pi r[/tex] so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.
1c. Area=[tex]\pi r^{2}[/tex] so first do the radius by the second power, or [tex]r * r[/tex], susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in
Sorry I could not answer every question but hope this helps!
Matt's four cousins are coming to visit. There are four identical rooms that they can stay in. If any number of the cousins can stay in one room, how many different ways are there to put the cousins in the rooms
The total number of different ways there are to put the cousins in the rooms is; 15
How to use probability combinations?When we count the number of cousins staying in each room, it means that the possibilities are as follows; (4,0,0,0), (3,1,0,0), (2,2,0,0), (2,1,1,0), (1,1,1,1).
1) (4,0,0,0): This means that there is only 1 way to put all the cousins in the same room due to the fact that the rooms are identical.
2) (3,1,0,0): This means that there are 4 ways to choose which cousin will be in a different room than the others.
3) (2,2,0,0): This means that there are 3 ways to choose which of the other cousins will also stay in that room, and then the other two are automatically in the other room.
4) (2,1,1,0): This means that the number of ways to choose which cousins stay in the same room is; 4C2 = 6
5) (1,1,1,1): This means that there is only one way for all the cousins to the total number of possible arrangements is;
1 + 4 + 3 + 6 + 1 = 15each stay in a different room.
Therefore, the total number of possible arrangements is;
1 + 4 + 3 + 6 + 1 = 15
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If you played 12 games but only won 7, what is the percent of the victories?
Answer:
58.3%
Step-by-step explanation:
7/12 = 0.583333333
0.583333333 simplified is 58.3%
Answer:
Approximately 58.3%.
Step-by-step explanation:
7/12 ≈ 0.583
0.583 = 58.3%
You’ve gone to visit your friend in Germany. As you’re getting dressed for a day out, your friend tells you it’s 16 degrees (Celsius) outside. The formula for degrees Celsius in relation to degrees Fahrenheit is
C=(5f-160)/(9)
a. Invert this equation to solve for Fahrenheit.
b. Tell what the temperature is in degrees Fahrenheit.
c. What kind of clothing should you wear for the day to be comfortable at that temperature?
d. Is there a temperature at which Celsius and Fahrenheit are described by the same number? Explain how you would find that number.
The volume, in cubic centimeters, of a fish
tank is represented by the polynomial
model
The polynomial's maximum value is relative.
Is the maximum relative or absolute?Here we have the polynomial:
[tex]V(x) = 36x^2 - 3.75x^3[/tex]
Notice that the leading coefficient is negative, so, as x tends to negative infinite, V(x) will tend to positive infinite.
So we only have a relative maximum, because is local maximum (at x = 6.4), but the function can take larger values than that.
You can also check that on the graph of V(x), which you can see below:
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A system of linear equations is given by the tables. one of the tables is represented by the equation . x y 0 5 3 6 6 7 9 8 x y -6 9 -3 8 0 7 3 6 the equation that represents the other equation is y = x . the solution of the system is ( , )
The solution of the system would be (3,6).
Lets solve the problem,
Other equation: y = 1/3x+5
Slope-Intercept Form: y = mx + b
Slope Formula:
y2-y1/x2-x1 = m
Have to find equation now:
m = (6 - 5)/(3 - 0)
m = 1/3
y = 1/3x + b
5 = 1/3(0) + b
b=5
y = 1/3x + 5
Lets put the substituition method here,
1/3x + 5 = -1/3x + 7
2/3x + 5 = 7
2/3x = 2
x = 3
y = 1/3(3) + 5
y = 1 + 5
y = 6
Therefore the coordinates are (3,6)
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Hi! I’ve tried at this question many times and still do not understand why the answer isn’t B but A. Please explain as best as you can! Thanks! (The question is below in the picture)
Answer:
Graph B is not linear.
Step-by-step explanation:
This question asks for a linear relationship. Graph B is not linear.
Please look closely at the attached images where I gave graphed these points.
I hope this helps. Please let me know if you have questions.
Go to a clothing store with
your parent/guardian and
pick out one item that you
would like to purchase. How
much of a discount would
you have if the item had
25% off sale? What would
a
the sale price be?
Answer:
original price $75
discount $18.75
sale price $56.25
Step-by-step explanation:
I found a pair of dress pants for $75.
Since the discount is 25%, then the discount is
25% of $75 = 0.25 × $75 = $18.75
The sale price is the original price, $75, minus the discount, $18.75.
$75 - $18.75 = $56.25
Which term best describes the figure shown below?? WILL MARK BRAINLIEST!!!
Answer:
Line LM
Step-by-step explanation:
Answer:
A line is a straight path on a plane that extends forever in both directions with no endpoints.
The answer will be lineLM
y = x + 3 what is the the graph lines for this ?
Answer:
screenshot attached of graph
Step-by-step explanation:
It cost jose $8.70 to send 87 text messages how much will it cost to send 10 text messages
Answer:
$1.00 = 10 cent each
Step-by-step explanation:
These cones are similar. Find the surface area of the smaller cone. Round to the nearest tenth. 3cm 2 cm. Help!!!
Answer:
33.3
Step-by-step explanation:
The scale factor is 2/3.
The ratio of the surface areas is the square of the scale factor, so the surface area of the smaller cone is 75(2/3)², which is about 33.3 cm²
the price of an all access take it to the fair is $42.99 before tax roland bought the all access ticket for 40% off then he pay 7% sales tax on the discounted price part a how much did roland paid in sale tax? part b what is the total amount that roland paid for the ticket ?
The total amount that roland paid for the ticket is $27.60
Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.
We need to calculate the total amount paid by the roland
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100
The price after 40% off -
= 42.99*60% = $25.794
Sales tax on 25.794
= 25.794*7% = $1.80558
Total amount Paid for the ticket
= 1.80558 + 25.794 = $27.59958
= $27.60
Hence the total amount paid by roland is $27.60
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Multiplica: (5 ft 6 in) x 4.
Answer: 22 ft
Step-by-step explanation:
Which of the following is the graph of the quadratic function y = x² - 6x-16?
++
10
-10
10-
-20-
-10
-10-
4
10
-10
O A. Graph A
OB. Graph D
C. Graph B
O D. Graph C
10
-10-
B.
10
10
D.
10
Answer:
C
Step-by-step explanation:
Graph C is the only one that has a y-intercept of (0, -16): note that when x = 0, y = 0^2 - 6(0) - 16, or y = -16 when x = 0.
can anyone solve this 100+3-4(4-5) divided by 6+5+5+5+300
One number is 4 more than another and their sum is 60.
If x = the larger number and y = the smaller number, then which of the following is the value of the smaller number?
The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding
Calculate the value of the numbers:Given that one number is 4 more than another,
⇒x = y + 4 (equation (1))
Their sum is 60,
⇒x + y = 60
y + 4 + y = 60 (From (1))
2y + 4 = 60
2y = 56 ⇒ y = 28
x = y + 4 = 28 + 4 = 32
Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.
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Need Help with this question
Answer:
23/35
Step-by-step explanation:
there's 12 red cards and 23 black cards
total = 35 cards
probability to pick a black card = 23/35
Answer: 23/35
Step-by-step explanation:
Probability is the measure of the likelihood of an event occurring. It is measured by the number of favorable outcomes over the total number of possible outcomes.
Here, the event is a black card being drawn. Since there are 12 + 23 = 35 cards in the deck, there are 35 possible outcomes of what card is picked. Out of those 35 cards, 23 are black, making 23 of the 35 options be the option we want.
23 black cards out of 35 total cards can also be written as [tex]\frac{23}{35}[/tex], which is the probability that a black card is chosen.
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the
next few hours, the temperature drops 2 degrees every hour.
Which equation represents the temperature, t, at hour h?
OA. t= 2h+32
B. t= -2h+ 32
C. t = 32h-₂
OD. t= -32h+2
You would multiply the change per hour by number of hours to get -2h
That would be added to the starting temperature.
Answer: B, t = -2h + 32
Answer: The answer is B
Step-by-step explanation:
The question says it drops ( which means subtraction) by 2 degrees every hour, so -2h
A recipe for fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice. Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice. Which recipe will have the stronger pineapple taste
The jo's drink have stronger pineapple taste.
Given that fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice and Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice.
In the Recipe for fruit punch calls
The Number of liters of orange juice = 333.
The Number of liters of pineapple juice = 222.
Thus, Total number of liters of juice = 222+333= 555 liters
Now, % of pineapple juice in fruit punch is
P₁=(222/555)×100
P₁=0.4×100
P₁=40%
Further, % of orange juice in fruit punch is
O₁=(333/555)×100
O₁=0.6×100
O₁=60%
In Jo's drink
The Number of liters of orange juice = 444.
The Number of liters of pineapple juice = 333.
Thus, Total number of liters of juice = 444+333= 777 liters
Now, % of pineapple juice in jo's drink is
P₂=(333/777)×100
P₂=0.43×100
P₂=43%
Further, % of orange juice in jo's drink is
O₂=(444/777)×100
O₂=0.57×100
O₂=57%
Hence, the taste of both drinks was not the same, jo's drink will have a stronger pineapple taste and jo's drink will have a lesser orange taste.
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Which could be the missing data item for the given set of data if the median of the complete data set is 15?
11, 23, 12, 18, 11, 10, 19, 15, 19, 21, 13, 17, 24, 14
A. 16
B. 18
C. 20
D. 11
The missing data item for the given set of data if the median of the complete data set is 15 is 11; option F
MedianMedian = 15Mission data = nData set: 11, 23, 12, 18, 11, 10, 19, 15, 19, 21, 13, 17, 24, 14
Median = Sum of data + n / number of data
15 = (11+23+12+18+11+10+19+15+19+21+13+17+24+14) + n / 15
15 = 214 + n / 15
15 × 15 = 214 + n
225 = 214 + n
n = 225 - 214
n = 11
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model aeroplane is made to a scale of 1 by two of the size of the real plane the area of the wings of the real plane are 40 m square find the area of the wings of the model in centimetre square
The area of the wings of the model is 100000 square centimeters
How to determine the model area of the wings?The given parameters are:
Scale factor, k = 1/2
Actual area of wings, A = 40 square meters
The model area is calculated as
Model area = Actual area * k^2
This gives
Model area = 40 * (1/2)^2
Evaluate
Model area = 10 square meters
Convert square meters to square centimeters
Model area = 10 * 10000 square centimeters
Evaluate
Model area = 100000 square centimeters
Hence, the area of the wings of the model is 100000 square centimeters
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The triangles are similar. Find the value of the variable.