enter a 3x3 skew symmetric matrix A

Question

enter a 3 times 3 skew-symmetric matrix A that has entries a₂₁=0, a₁₃=1, a₃₂=2.

 

 

Answer 1

Skew symmetric matrices mean that A (transpose) = -A, So since you know 3 elements of the matrix, you know the 3 symmetric to them over the main diagonal mut be the negatives of those elements. The main diagonal itself must all be 0s. The main diagonal gets transposed onto itself. 0s is the only way A can become -A.So we;ve got

 

0     0    1

0     0    -2

-1    2    0

 

Let's see if this really works!

 

A transpose is

0   0   -1

0   0   2

1  -2   0

 

-A would be

0   0   -1

0   0   2

1  -2   0

 

These are the same so the answer is correct.

Hope this helped.