Assume that T is a linear transformation. Find the standard matrix of T. T 6 T: R² R², rotates points (about the origin) through radians. A= (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed.)

Please box answer and write it in the same format as the question. Do not type it out only hand written. The question has to be a whole number not square root.

Describe all solutions of Ax 0 in parametric vector form, where A is row equivalent to the given matrix. %3D 1 40 -5 3 12 0 -15 x-X+X +x (Type an integer or fraction for each matrix element.) Enter your answer in the edit fields and then click Check Answer. All parts showing Type here to

Find the inverse matrix. Must show work and label each step as a linear combination of row transformation (example: -R1+R2) or unchanged.

Let A = [1 -1 -1              -1   1 -1              -1  -1  1]. Find a diagonalization if possible.

H.W Find the inverse to the following matrices by using adjoint method. 1 31 b. A = 2 0. 1 1 1

Consider the following matrix and vector: 1 1 1 -4 0 -3 A = -2 and x= x3 Given that Ax=0 and x3=-1, find x2. O-1 O1 2 O-2

Find the inverse of the matrix A = A-1 ab = (²24) 3). sin (a) f di an B Pa

Use determinant to decide if the following vectors are linearly independent: -8 7 -4 -6 7 -5

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 x, -axis. A-0 (Type an integer or simplified fraction for each matrix element)