Question

Mark each statement True or False. Justify.

1. A linear transformation T W Rn ! Rm is completely determined by its effect on the columns of the n * n identify matrix.
A. True
B. False
2. If A is a 3 * 2 matrix, then the transformation x Ax cannot be one-to-one.
A. TrueB. False

Answer 1

1. A. True

2. B. False

Explanation:

The columns of the identity matrix are basis vector in Rn. Every vector can be written as linear combination and T is linear transformation. The transformation map can be from R2 to R3. It can be one to one. If A is 3*1 matrix, then transformation x Ax can not be R2 onto R3. Properties of linear transformations are preserved under rotation.