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Question

Mathematics Question on Matrices

if A=[2x0 xx]A=\begin{bmatrix}2x&0\\\ x&x\end{bmatrix} and A−1=[10 −12],thenxequalsA^{-1}= \begin{bmatrix}1&0\\\ -1&2\end{bmatrix},then x equals

A

22

B

−1/2-1/2

C

11

D

1/21/2

Answer

1/21/2

Explanation

Solution

A=[2x0 xx],A−1=[10 −12]A=\begin{bmatrix}2x&0\\\ x&x\end{bmatrix}, A^{-1}= \begin{bmatrix}1&0\\\ -1&2\end{bmatrix} We know that, AA1=IAA^{1} =I ⇒[2x0 xx][10 −12]=[10 01]\Rightarrow \begin{bmatrix}2x&0\\\ x&x\end{bmatrix}\begin{bmatrix}1&0\\\ -1&2\end{bmatrix} = \begin{bmatrix}1&0\\\ 0&1\end{bmatrix} ⇒[2x0 02x]=[10 01]\Rightarrow\begin{bmatrix}2x&0\\\ 0&2x\end{bmatrix}=\begin{bmatrix}1&0\\\ 0&1\end{bmatrix} On comparing, we get 2x=1⇒x=122x = 1 \Rightarrow x= \frac{1}{2}