Practice question · Select all that apply
The diagonal matrix with rows (5, 0) and (0, -1) acts on the plane. Select every TRUE statement.
Hints
- Apply the matrix to each axis vector.
- Check whether A(1,1) stays parallel to (1,1).
Show the answer
- A. It stretches the x-direction by 5
- B. It flips the y-direction
- D. (0, 1) is an eigenvector with eigenvalue -1
- E. (1, 0) is an eigenvector with eigenvalue 5
Why
The axis vectors are eigenvectors: (1,0) scales by 5, (0,1) by -1 (a flip). But A(1,1) = (5,-1), which is not a multiple of (1,1), so (1,1) is not an eigenvector.
Practise Eigenvalues and Eigenvectors
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