Let T Ꮖ 4y- - x = 4x+5y+7z (a) Find the standard matrix of this linear transformation T. (b) Find T 3 (4) (c) Find all preimages x where T(x) : = 3 0

Consider a linear transformation T from R2 to R² for which (:) -}- T and T Find the matrix A of T. A =

Identify the matrix that represents each linear transformation below. Write A, B, C, D, D or F. 20 -2 0 A = B= = 02 0 -√212 √212 (39), ^ - (² :) " - ( - ² - 2).C-( √²/2 √212) P-(-03). E-(0-²). 2 D= E= 20 and F= √212-√212 √212 √212 1. Clockwise rotation by an angle of 450 is associated to matrix 2. Counterclockwise rotation by an angle of 45° is associated to matrix 3. Clockwise rotation by an angle of 90° is associated to matrix 4. Counterclockwise rotation by an angle of 900 is associated to matrix 5. A dilation by a factor of 2 is associated to matrix 6. Reflexion about the origin and a dilation by a factor of 2 is associated to matrix Hint: Draw a vector and its image under each transformation.

Let 4-[1] and W-[*] A = w= -[-1³]. Find k so that there exists a vector X whose image under the linear transformation T(x) = Axis w. Note: The image is what comes out of the transformation. k = Find k so that w is a solution of the equation Ax = 0. k =

Find the matrix A of the linear transformation from R2 to R' given by 5 T 6 x1 + -1 x2. %3D -8 7 A =

5. Determine the matrix of the transformation that first reflects points through the horizontal x-axis and then reflects points through the line y = x.

Define the linear transformation T: R²-> TR² vin T (5) = (2x-²4) Find the matrix representation of the Inverse function of T.