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Let A = 5 9
2 7
and B = 1 8
3 6
Find the standard matrix C of the linear transformation T(x) = B(A(x)).
And then
Determine which of the formulas hold for all invertible n×n matrices A and B
A. A5 is invertible
B. (ABA−1)8 = AB8A−1
C. (A+B)(A−B) = A2−B2
D. (A+A−1)3 = A3+A−3
E. A+In is invertible
F. ABA−1 = B
And finally
Which of the following linear transformations from R3 to R3
are invertible?
A. Projection onto the xz -plane
B. Projection onto the x -axis
C. Rotation about the z -axis
D. Identity transformation (i.e. T(v) = v for all v)
E. Dilation by a factor of 6
F. Reflection in the y -axis
>_> Too hard.
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