Linear Algebra

Matrix A shown below is associated with a linear transformation and T(x)= Ax

1 3

A =

2 5

1. Find

1

T

0

0

T

1

2. Find

2

T

3

1

T

1

3. Linear Transformation T is a mapping from R2 → R2 and if T is onto then for every b

in R2 there is at least one x in R2 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 R2 → R2 and if T is one-to-one then the only value in R2 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

x1 − 2x2

x1

T = x1 − 3

x2

2x1 − 5x2