Thread: Matrix question.

If A is a 2X2 matrix, a12 = a21 = 0, a11 ≠ 0, a22 ≠ 0 then show that A is regular and find A^-1.
Many thanks in advance.

Originally Posted by grooverandshaker

If A is a 2X2 matrix, a12 = a21 = 0, a11 ≠ 0, a22 ≠ 0 then show that A is regular and find A^-1.
Many thanks in advance.

A matrix is regular if it has an inverse. How can you tell if a matrix has an inverse? (Hint: Think of what the determinant of a singular matrix is.)

-Dan

Um, I know that a matrix has an inverse if the determinant is nonzero. Is that right?
I usually know how to find the determinant and the inverse but I just can't do it when the matrix isn't written out.
Could you help me figure out what the original matrix is?

Given that a12 and a21 are both 0 and that a11 and a22 are not 0, the matrix must have a nonzero determinant. There are no values of a11 and a22 that can make the determinant 0.

Originally Posted by grooverandshaker

Um, I know that a matrix has an inverse if the determinant is nonzero. Is that right?
I usually know how to find the determinant and the inverse but I just can't do it when the matrix isn't written out.
Could you help me figure out what the original matrix is?

This page seems to be a good guide in general. It has an explicit answer for the 2 x 2 case, but make sure you understand how to do the problem in general.

-Dan

Thanks guys. I think I understand now.