Question:
if $A=\begin{bmatrix}2x&0\\ x&x\end{bmatrix}$ and $A^{-1}= \begin{bmatrix}1&0\\ -1&2\end{bmatrix},then x equals$
if $A=\begin{bmatrix}2x&0\\ x&x\end{bmatrix}$ and $A^{-1}= \begin{bmatrix}1&0\\ -1&2\end{bmatrix},then x equals$
Updated On: Jul 6, 2022
- $2$
- $-1/2$
- $1$
- $1/2$
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The Correct Option is D
Solution and Explanation
$A=\begin{bmatrix}2x&0\\ x&x\end{bmatrix}, A^{-1}= \begin{bmatrix}1&0\\ -1&2\end{bmatrix} $
We know that, $AA^{1} =I $
$\Rightarrow \begin{bmatrix}2x&0\\ x&x\end{bmatrix}\begin{bmatrix}1&0\\ -1&2\end{bmatrix} = \begin{bmatrix}1&0\\ 0&1\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2x&0\\ 0&2x\end{bmatrix}=\begin{bmatrix}1&0\\ 0&1\end{bmatrix}$
On comparing, we get $2x = 1 \Rightarrow x= \frac{1}{2}$
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.