Considere los polinomios pi(t) = 1 + 1, p2(t) = 1-1, P3(1) =
4, p4(1) = 1 + 7, y Ps(1) = 1 + 2t + 7, y sea H el subespacio
Ps generado por el conjunto S = (Pi P2. P3 P4. Ps). Utilice el
método descrito en la demostración del teorema del conjunto generador (sección 4.3) para producir una base de H. (Expli-que cómo seleccionar los elementos apropiados de S.)

Therefore, We can use the Gaussian elimination method to find the basis of H.

In linear and multilinear algebra, the procedure of Gauss elimination involves first solving one of the simultaneous linear equations for one variable (in terms of all the others) and then substituting this expression into the other equations to discover the answers.

A linear equation is an algebraic equation in which each term has an exponent of 1, which, when plotted on a graph, always yields a straight line. One example with one variable is where ax+b = 0, where a and b are fundamental values and x is the variable.

Selecting the polynomials Pi(t) = 1 + t and P2(t) = 1 - t from the set S. These are linearly independent since they cannot be written as a linear combination of the other polynomials in the set and checking if the span of Pi(t) and P2(t) is equal to H. Then expressing the remaining

polynomials P3(t), P4(t), and Ps(t) in terms of Pi(t) and P2(t) and checking if they can be written as a linear combination of Pi(t) and P2(t) or not.

P3(t) = 4 can be written as 4 * Pi(t) - 4 * P2(t)

P4(t) = 1 + 7t can be written as Pi(t) + 7 * P2(t)

Ps(t) = 1 + 2t + 7t^2 can be written as Pi(t) + 2t * P2(t) + 7 * P2(t)^2

From this, we can see that all the polynomials in S can be written as a linear combination of Pi(t) and P2(t). So, the span of Pi(t) and P2(t) equals H. Hence, { Pi(t), P2(t) } is a basis for the subspace H.

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