First slide

Applications of determinant

Question

$If [\begin{array}{cc} x & y^{3} \\ 2 & 0 \end{array}] = [\begin{array}{ll} 1 8 \\ 2 0 \end{array}], Then {[\begin{array}{ll} x y \\ 2 0 \end{array}]}^{- 1} =$

Moderate

A

$[\begin{matrix} 0 & - 2 \\ - 2 & 1 \end{matrix}]$
B

$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
C

$[\begin{matrix} 0 & - 8 \\ - 2 & 1 \end{matrix}]$
D

$[\begin{matrix} 0 & 1 / 2 \\ 1 / 2 & - 1 / 4 \end{matrix}]$

Solution

$\begin{array}{l} [\begin{array}{ll} x & y^{3} \\ 2 & 0 \end{array}] = [\begin{array}{ll} 1 & 8 \\ 2 & 0 \end{array}] \\ \Rightarrow x = 1, y = 2 \\ {[\begin{array}{ll} x & y \\ 2 & 0 \end{array}]}^{- 1} = {[\begin{array}{ll} 1 & 2 \\ 2 & 0 \end{array}]}^{- 1} = \frac{1}{0 - 4} [\begin{array}{cc} 0 & - 2 \\ - 2 & 1 \end{array}] = [\begin{array}{cc} 0 & 1 / 2 \\ 1 / 2 & - 1 / 4 \end{array}] \end{array}$

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