• February 23rd 2010, 01:42 PM
The question is Asking to find A And Adj A when we have both with some missing entries.

A =
2 1 4
3 / /
1 / /

/ / -1
/ 8 /
/ 3 1

First Column is empty in Adj A.

The questions asks to find A and Adj a by finding the missing entries which i denoted here by using the symbol ( / )

• February 24th 2010, 04:11 AM
tonio
Quote:

The question is Asking to find A And Adj A when we have both with some missing entries.

A =
2 1 4
3 / /
1 / /

/ / -1
/ 8 /
/ 3 1

First Column is empty in Adj A.

The questions asks to find A and Adj a by finding the missing entries which i denoted here by using the symbol ( / )

For example look at the 2-2 entry in $Adj \,A$ , which is 8: this entry is the determinant of the minor $A_{22}$ of the original matrix, i.e.: "erase" the second row and
the second column of A and calculate the determinant of the remaining 2x2 matrix: we get $A_{22}=\det\begin{pmatrix}2&4\\1&x\end{pmatrix} \Longrightarrow 8=2x-4\Longrightarrow x=6$ and we've found