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

Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: Jx1, х2) %3D (Зхі — 5х2, —6х1 + 10x), K(x1, x2) = (-V3x2, 3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (Зх1 + 5х, бх1 — бх2), N(x1, x2) = (-v5x1, v5x2). (a) In each case, compute the determinant of the transformation. . det J= ,det K ,det L= ,det M= ,det N

You need to rotate point bP1=n [10 10 0] 60 degrees on the X axis and 10 units on the Z axis. Write the transformation matrix and graph of the resulting vector

all of part (a) please

Set up the matrix which will perform the following transformation and write down its character.(x -y)to(y -x)

Find the global transformation matrix to transfer the local coordinate system (x1, y1, z1) to the global coordinate system (X0, Yo, Zo).

Let f be the linear transformation represented by the matrix A = 4-(32) Find the point (x, y) such that f(x, y) = (-4,-1). (Give your answer exactly, not as a decimal approximation.) The point is

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 =

Let T: R² R² be given by Find the matrix M of the inverse linear transformation, T-¹. M = T(x) »=[7]× -3 4 -5 X.

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