# Linear Algebra: Finding Determinant Using the Cramer's Ruler

• October 9th 2007, 05:18 AM
googoogaga
Linear Algebra: Finding Determinant Using the Cramer's Ruler
Hello, I have a homework problem that I am not seeing quite well. Please help somebody.

1) Let A be a 4 by 4 matrix. If

2 0 0 0
0 2 1 0
0 4 3 2
0 -2 -1 2

find A.

Answer from back of the book:

A=
1 0 0 0
0 4 -1 1
0 -6 2 -2
0 1 0 1

*I have no clue on how to go from Adjoint A to A.
• October 9th 2007, 06:28 AM
topsquark
Quote:

Originally Posted by googoogaga
Hello, I have a homework problem that I am not seeing quite well. Please help somebody.

1) Let A be a 4 by 4 matrix. If

2 0 0 0
0 2 1 0
0 4 3 2
0 -2 -1 2

find A.

Answer from back of the book:

A=
1 0 0 0
0 4 -1 1
0 -6 2 -2
0 1 0 1

*I have no clue on how to go from Adjoint A to A.

You may find this site helpful.

-Dan
• October 9th 2007, 08:20 AM
googoogaga
I still don't understand because the matrix in the site is a 3 by 3 matrix. I just can't see it. Please I would like to see the steps. thanks
• October 9th 2007, 08:28 AM
topsquark
Quote:

Originally Posted by googoogaga
$A_{11} = \left | \begin{matrix} 2 & 1 & 0 \\ 4 & 3 & 2 \\ -2 & -1 & 2 \end{matrix} \right | = 4$