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a)

If A =

1 2

0 3

and B is an upper-triangular matrix such that tr(B) = 0 and

AB =

1 -1

0 -3

then B = _____

AND

b)

If A =

1 5

-1 3

and A = B+C where B is symmetric and C is skew-symmetric, then

B = ___ and C = ____.

2)

a)

If A, B and C are matrices such that A^TB^(-1)C is a column matrix, and A is a 2x5 matrix, then the size of B is _____ and the size of C is ___.

b)

If B^(−1)A^TBC is a 6 × 7 matrix, then the size of A is ,

the size of B is ___, and the size of C is ____.

Are there some easy techniques that can be used to find the sizes of each of the matrix, such as 2a and 2b? I kind of have an idea of how to do those mentioned in 1a but 1b having a bit trouble. These are not homework questions but questions from old exams. I have an exam coming up and I'm trying to review. Any suggestions would be much appreciated. Thank you

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# Techniques for solving type of Matrix problems

Can you offer guidance or do you also need help?

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