Techniques for solving type of Matrix problems

[niteshadw]

1)
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

 

[member 553083]

!1a) B =0 00 0C = 0 -11 01b) B = 3 22 4C = 0 1-1 02a) The size of B is 5x5 and the size of C is 2x5.2b) The size of A is 6x5, the size of B is 5x7, and the size of C is 7x7.