The set B = {4- 2x², 12 + 3x − 6x², 18x² - (35 + 6x)} is a basis for P₂. Find the coordinates of p(x) = 72x2 - (140 +27x) relative to this basis: [p(x)]B =

Consider the basis B= {1, x+x?, 2x²-1} for the vector space P2. The coordinate vector of the polynomial p(x) = 7 + 5x + 4x2 relative to B is B

In P,, find the change-of-coordinates matrix from the basis B = {1 + 5t, - 6+t- 29t,1 - 6t} to the standard basis. Then write t as a linear combination of the polynomials in B. find the change-of-coordinates matrix from the basis B to the standard basis. In P2: 1 - 6 1 1 - 6 C-B 5 - 29 (Simplify your answer.) Write t as a linear combination of the polynomials in B. ? =(1+5?) +(-6+t-291) +1 – 6t) %3D (Simplify your answers.)

The set B = {-(2 + 2x²), - (6+4x+6x²), 18 + 8x + 16x²} is a basis for P₂. Find the coordinates of p(x) = - (32 + 8x +26x²) relative to this basis: [p(x)] B =

find a basis for the range from r2 to r3 as defined by [3x1+4x2; x1-2x2; 4x1]

The set B = {− (3 + 4x²), − (6 + 3x + 8x²), 8 + 6x + 8x²} is a basis for P₂. Find the coordinates of p(x) - [p(x)]B = (56 +30x + 64x²) relative to this basis:

The set B={[−1010],[00−11],[0002]} is a basis of the space of upper-triangular 2×2 matrices. Find the coordinates of M=[−60−4−5] with respect to this basis.