III. Consider the bases for M2x2(R) given by a' : and a the stan- dard basis. Consider the basis for P, given by B' : x² + x,x – 1, x+1 and B the standard basis. Find the following: iv. the change of coordinate matrix from 3' to B For the transformation T : M2x2(R) → P2 given by T = (a+2b)x² + (b+3c)x+c+4d find the following: v. [Ta vi. [T

Use the following theorem: If T:Rn Rm is a linear transformation, and e₁,e2, en are the standard basis vectors for Rn, then the standard matrix for T is [T] = [T(e₁)_T(е₂) T (en)] Find the standard matrix for T:R³ → R³ from the images of the standard basis vectors. T:R³ → R³ reflects a vector about the xy -plane, then reflects that vector about the xz -plane, and then reflects that vector about the yz -plane. i MO ...