The answer should be A a 3x3 matrix Also please include all

The answer should be A (a 3x3 matrix)

Also please include all steps clearly thank you!

(1 point) The cross product of two vectors in R is defined by a2b3 a3b2 a3b1 a1b3 a X b a1b2 a2b1 Let v 8 Find the matrix A of the linear transformation from R to Rs given by

Solution

Let X = (x,y,z)^T. Then T(X) = v x X = (x,y,z)^T x ( -8,8,-8)^T = ( -8y -8z, -8z+8x, 8x+8y) = AX, where A =

0

-8

-8

8

0

-8

8

8

0

The above matrix A is the required matrix.

0	-8	-8
8	0	-8
8	8	0