First slide

Applications of determinant

Question

Let $A = [\begin{matrix} 2 & - 1 \\ 3 & 4 \end{matrix}], B = [\begin{matrix} 5 & 2 \\ 7 & 4 \end{matrix}], C = [\begin{matrix} 2 & 5 \\ 3 & 8 \end{matrix}]$ .Let D be a matrix such that CD=AB, then D equals

Easy

A

I
B

O
C

-A
D

none of these

Solution

$C D = A B \Rightarrow D = C^{- 1} (A B)$
Now $A B = [\begin{array}{cc} 2 & - 1 \\ 3 & 4 \end{array}] [\begin{array}{ll} 5 2 \\ 7 4 \end{array}] = [\begin{array}{cc} 3 & 0 \\ 43 & 22 \end{array}]$ and
$\begin{array}{l} C^{- 1} = [\begin{array}{cc} 8 & - 5 \\ - 3 & 2 \end{array}] \\ D = [\begin{array}{cc} 8 & - 5 \\ - 3 & 2 \end{array}] [\begin{array}{lc} 3 & 0 \\ 43 & 22 \end{array}] = [\begin{array}{cc} - 191 & - 110 \\ 77 & 44 \end{array}] \end{array}$

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