Linear Math

Quiz 2

Due back by Friday, June 28

Matrix A shown below is associated with a linear transformation and Tx  Ax

A  1 3

2 5

1. Find

T 1

0

T 0

1

2. Find

T 2

3

T 1

1

3. Linear Transformation T is a mapping from 2 → 2 and if T is onto then for every b in 2 there is at least one x in 2 where Tx  b. or said with matrices

Ax  b has a solution for every possible b. Determine if T is "onto" or not.

4. Linear Transformation T is a mapping from 2 → 2 and if T is one-to-one then the only value in 2 where Tx  0. is x  0 or said with matrices

Ax  0

Determine if T is one-to-one or not.

5. Show that the following Linear Transformation is NOT linear

T x1

x2 

x1 − 2x2 x1 − 3

2x1 − 5x2