4. Let P2 {ao +ait+azt | a0, a1, a2 E R}. That is, P2 is the linear space of all polynomials of degree less than or equal to two. Let L: P P2 be the linear transformation defined by L(f(t)) = f(0) + f(3)t. For example, L(1+2t+3t2) (1 + 2(0) + 3(0)2) + (1+2(3) +3(3)²) t = 1+34t. Similarly, L(1) = 1+t and L(t) = 3t. %3D (a) Find L(t2) = (b) Assume that L is a linear transformation and that A = {1,t, t2} is the standard basis for P2. Give the definition of [La and then find it. (c) The set C = {1-t2,1 + 2,1+t+ t2} is another basis for P2. Find the change of basis matrix P such that (L]e = P '(L]aP.

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.