Question 38

If inverse of the matrix $$\begin{bmatrix}2 & -0.5 \\-1 & x \end{bmatrix}$$ is $$\begin{bmatrix}1 & 1 \\2 & 4 \end{bmatrix}$$, then the value of x is

Solution

We know that $$AA^{-1}=I$$

=> $$\begin{bmatrix}2 & -0.5 \\-1 & x \end{bmatrix}\begin{bmatrix}1 & 1 \\2 & 4 \end{bmatrix}=\begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix}$$

=> $$\begin{bmatrix}1 & 0 \\ -1+2x & -1+4x \end{bmatrix}=\begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix}$$

=> $$-1+4x=1$$ => $$x=0.5$$

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