The standard matrix for the linear transformation t is
| 3 6 |
| 3 -6 |
How to determine the standard matrix for the linear transformation t?
The linear transformation of matrix T is given as:
t(x, y) = (3x + 6y, 3x − 6y)
When the above linear transformation is represented as a matrix, we have the following expression
T([x]) = | 3x + 6y |
[y] | 3x - 6y |
The above linear transformation of matrix can be rewritten as the following product of matrixes
T([x]) = | 3x + 6y | = | 3 6 | | x |
[y] | 3x - 6y | | 3 -6 | | y |
From the above equation, the standard matrix for the linear transformation t is
| 3 6 |
| 3 -6 |
Hence, the standard matrix for the linear transformation t is
| 3 6 |
| 3 -6 |
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