Let T : R? → R² be the linear transformation that projects vectors onto the line y = -x and then rotates the result by 180 degrees about the origin. (a) Find the matrix that induces T. (b) It T invertible? Explain your reasoning.

Answer it entirely please. Thanks

Write down the matrix A that represents the linear transformation f : R² → (a) R² (i.e. so that f(x) = Ax) that rotates anti-clockwise about the origin by an angle 7/2.

please solve part d

Which of the following are linear transformations?

Find the image of the point (x, y) under the matrix transformation that first reflects the point with respect to the x-axis, then rotates the resulting point about the origin through an angle of T/3, and then reflects the resulting point with respect to the line y = x.

(c) Find the rotation matrix of a linear transformation T: R² R², which first rotates points 3 clockwise and then reflects points through the z-axis. -

Linear algebra review number 1

Find the kernel of the linear transformation. (If all real numbers are solutions, enter REALS.) T: R* - R*, T(x, y, z, w) = (z, x, w, y) ker(7) = { REALS :X, Y, z, w ER

Solve the problem. 2 3 1 Let A = S -7 5 Define a transformation T: R³ 24-49 10 30 -28 12 O O O 18 42 O 29 -15 < Previous and u = 2 by T(x) = Ax. Find T(u), the image of u under the transformation T