Let T be the linear transformation from R³ to R³ defined by 1 W1 (C) H G] -1 - W2 4 W3 Find the matrix representation for this transformation. T Hint: proj, (w) = proj(w), where 7 = = w.v - (v) ||||²

Consider a linear transformation T from R³ to R² for which Find the matrix A of T. +46 A = T (B)-· *(B)-· *(8) - A T T

Find the matrix A of T. A= Consider a linear transformation T from R³ to R² for which = E T = [8]. T = T * (E) - · *(8) - · *(6) - A -H). =

Find the B-matrix for the transformation xAx, where B={b₁,b₂}- -5 - 1 2 = *[*) * * C A = b₁ b₂ 5 The B-matrix of the given transformation is

Find the matrix M of the linear transformation T: R² R² given by [H 9x1 + 3x₂ 671-7₂ T M =

Find the matrix A of the linear transformation T from R2 to R² that rotates any vector through an angle of 45° in the clockwise direction. A = 9-

Consider a linear transformation T from R? to R² for which 7 (C) - [- ma 7 (1) - [- (H)-- T and T Find the matrix A of T. A: %3D

assume that T is a linear transformation. Find a Standard matrix of T. T: IR² →IR" 8) where A T(e₁) = (5,1,5,1) T(e₂) = (-3₁7,0,0) ? e₁ = (1,0) € 2 = (0₁1) (integer or decimal)