LA2.1.6

Find the value of determinant of the matrix $\begin{bmatrix} 29 & 26 & 22 \\ 25 & 31 & 27 \\ 63 & 54 & 46 \end{bmatrix}\,$

Determinant is

$\begin{vmatrix} 29 & 26 & 22 \\ 25 & 31 & 27 \\ 63 & 54 & 46 \end{vmatrix}\,$

By $C_1-C_2,C_2-C_3\,$ (C1,C2 etc.are respective columns)

$\begin{vmatrix} 3 & 4 & 22 \\ -6 & 4 & 27 \\ 9 & 8 & 46 \end{vmatrix}\,$

$(3)(4)\begin{vmatrix} 1 & 1 & 22 \\ -2 & 1 & 27 \\ 3 & 2 & 46 \end{vmatrix}\,$

By $C_1-C_2,C_3-22C_2\,$ we get

$12\begin{vmatrix} 0 & 1 & 0 \\ -3 & 1 & 5 \\ 1 & 2 & 2 \end{vmatrix}\,$

Therefore the determinant is $12(-1)(-6-5)=132\,$