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#1 2007-03-20 14:51:04

MajikWaffle
Member
Registered: 2005-12-14
Posts: 11

Couple of Linear Algebra Matrix Questions

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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