Practice question · Put in order
Order the steps to find the matrix of a linear transformation T on the plane.
- Make that image the second column
- Make that image the first column
- Compute T of the second basis vector (0, 1)
- Compute T of the first basis vector (1, 0)
Hints
- The columns are the images of the basis vectors, in order.
- First basis vector gives the first column.
Show the answer
- Compute T of the first basis vector (1, 0)
- Make that image the first column
- Compute T of the second basis vector (0, 1)
- Make that image the second column
Why
Transform each basis vector and place its image as the corresponding column. Because T is linear, these two columns then reproduce T on every vector via matrix multiplication.
Practise Linear Transformations
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