First slide

Applications of determinant

Question

$The inverse of A = [\begin{array}{ccc} 3 & 5 & 7 \\ 2 & - 3 & 1 \\ 1 & 1 & 2 \end{array}] is$

Moderate

A

$[\begin{matrix} 7 & 3 & - 5 \\ 3 & 1 & - 2 \\ - 26 & - 11 & 19 \end{matrix}]$
B

$[\begin{matrix} 7 & 3 & - 26 \\ 3 & 1 & - 11 \\ - 5 & - 2 & 19 \end{matrix}]$
C

$[\begin{matrix} 3 & 2 & 1 \\ 5 & - 3 & 1 \\ 7 & 1 & 2 \end{matrix}]$
D

none

Solution

If A is the given matrix, then det A=3 (-6-1)-5(4-1)+7(2+3)
=-21-15+35
=-1
$A d j A = [\begin{matrix} - 7 & - 3 & 26 \\ - 3 & - 1 & 11 \\ 5 & 2 & - 19 \end{matrix}] ∴ A^{- 1} = [\begin{matrix} 7 & 3 & - 26 \\ 3 & 1 & - 11 \\ - 5 & - 2 & 19 \end{matrix}]$

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