If A is a 5x5 matrix, and A^T=-A , show that A is singular? 10 points?

Brittn

New member
If A transpose =-A,
Show that A is singular
please show any or all methods. I know you can compute determinant but I do not know how.








OTHER QUESTIONS I HAVE to study for an exam:(can you explain briefly or however you want, the following? especially number 6)


1) A is a 4x4 matrix
p(?)=-?(?+1)(?-3)(-?+1)

Is A diagonalizable?
Is A invertible?

TRUE OR FALSE

2)A homogeneous system Ax = 0 is always consistent
3)If a square matrix is diagonalizable, its eigenvalues are distinct
4)Every two similar matrices have the same trace.
5)Every two row equivalent matrices have the same determinant
6)
If A and B are invertible, (AB)^1 = A^1B^1
 
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