Teacher/User Name: DEMO Name:__________________________ Practice ProblemsBy Easy Worksheet Period: ________ Date: ____________

### Solve:

1) Given the transformation T(x1, x2) = ( 5x1 + 4x2 , -9x1 − 5x2 )
Show that T is a linear transformation by finding the matrix A that describes this transformation.

By Easy Worksheet

By Easy Worksheet

By Easy Worksheet

By Easy Worksheet

2) Find the standard matrix of the transformation T: ℜ2 → ℜ2 that first rotates counterclockwise by π/6 then reflects through the line x2 = x1
3) Given the transformation T(x1, x2) = ( -7x1, -15x2, 9x2, -12x2, 15x2, -9x1)
Find x such that T(x) = (0, -540, 324, -432, 540, 0)

By Easy Worksheet

By Easy Worksheet

By Easy Worksheet

By Easy Worksheet

4) Find the standard matrix of the transformation T: ℜ2 → ℜ2 that first reflects through the line x2 = -x1 then rotates counterclockwise by π/3

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