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

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 =

M = Find the matrix M of the linear transformation T: R³ → R² given by * ((:D) - T = 2x1x₂+(-7): 6x2 +7x3 (-7) * 3).

Q3: Determine the Transformation matrix that transfer the shown object to its final destination (Refer to Local Coordinates). (5,3) End (0,0) Start

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

Let T1 and T2 be linear transformations given by X1 ЗХ1 + 5x2 X2 -2x1 + 8x2 X1 -2x1 + 9x2 X2 5x2 Find the matrix A such that the following is true. (a) T1(T2(x)) = Ax A = (b) T2(T1(x)) = Ax A = (c) T1(T1(x)) = Ax A = (d) T2(T2(x)) = = Ax A =