Linear Algebra Examples

Determine if Linear [[4,-3],[3,1]][[x],[y]]=[[-3],[4]]
Step 1
The transformation defines a map from to . To prove the transformation is linear, the transformation must preserve scalar multiplication, addition, and the zero vector.
M:
Step 2
First prove the transform preserves this property.
Step 3
Set up two matrices to test the addition property is preserved for .

Step 4
Add the two matrices.
Step 5
Apply the transformation to the vector.
Step 6
Break the result into two matrices by grouping the variables.
Step 7
Since the transformation addition property does not hold, this is not a linear transformation.