Linear transformations we are trying to find the size of the

Linear transformations, we are trying to find the size of the standard matrix. the problems I\'m having trouble understanding are 12 and 13, and how I\'m thinking I\'m supposed to approach this is the other picture. Are we just finding the dimensions to this?

A=[1-31 Find all vectors v in R? thel sacisties Tiv)- -117 oe sew 12. A linear traaslomalior T : KG -s. wait .e lae size of the standard no such vertor v exisra. matrix of T? 13. A linear iransformation T : R7 R1, what is the size of the standard. matrix of T 14) Let T : R2 E2 be the linear crasformation that reflects each vertir across the line i ir. I.\"1. S : R2 R2 he the linear trnnsformatinn that projerts each vector orthogonally onto the y-axis.

Solution

if T is a linear transformation s.t. T : U--> V

THEN size(dimension) of T is dimV * dimU

so size of T = 6 * 5 in 12

size of T= 4 * 7 in 13