- #1

- 613

- 3

I attached the problem.

I only need help with part b), I provided part a) just to remind you guys what a orthogonal matrix was.

The only 2x2 matrix I can think of with a determinant of + or - 1 is something like

√1 0

0 1

The determinant of this would be √1 = + or - 1

The second part asks me to show that this matrix is not orthogonal thus A^-1≠A^T

A^T=

√1 0

0 1

To calculate A^-1 I set up the 2x2 matrix with the identify matrix on the right and reduce so the left becomes the I matrix.

√1 0 1 0

0 1 0 1

→

1 0 1/√1 0

0 1 0 1

But when I do this I get A^-1 =

1/√1 0

0 1

Is this still considered = to A^T =

√1 0

0 1

?

I only need help with part b), I provided part a) just to remind you guys what a orthogonal matrix was.

The only 2x2 matrix I can think of with a determinant of + or - 1 is something like

√1 0

0 1

The determinant of this would be √1 = + or - 1

The second part asks me to show that this matrix is not orthogonal thus A^-1≠A^T

A^T=

√1 0

0 1

To calculate A^-1 I set up the 2x2 matrix with the identify matrix on the right and reduce so the left becomes the I matrix.

√1 0 1 0

0 1 0 1

→

1 0 1/√1 0

0 1 0 1

But when I do this I get A^-1 =

1/√1 0

0 1

Is this still considered = to A^T =

√1 0

0 1

?