Find the standard matrix representation for each ofthe following linear operators: L is the linear operator that reflects each vector x in R2 about the x1 axis and then rotates it 90◦ in the counterclockwise direction.

Let A = 1 -2 5 7 0 1 3 2 3 4 -1 -2 -1 -2 3 5 Find the matrices B = ¹/(A + AT) and C = (A – A¹). What is the relation between A and B + C?

Assume that T is a linear transformation. Find the standard matrix of T. T: R² →R² first reflects points through the vertical X2-axis and then reflects points through the horizontal x₁-axis. A = (Type an integer or simplified fraction for each matrix element.)

Let A= {a;.a2,a3} and B = {b,.b2.b3} be bases for a vector space V, and suppose a, = 5b, - – 2b3. a. Find the change-of-coordinates matrix from A to B. b. Find (xlg for x= 5a, + 6a2 + az. a P B-A b. xlg =0 (Simplify your answer.)

Let V be the vector space of all (2 × 2) matrices. Determine whether the followingmatrices A, B, and C are linearly independent or dependent?A =(1 23 1 ), B =(3 −12 2 ), C =(1 −5−4 0 )