Question:
The matrix 'X' in the equation $AX = B$, such that $A = \begin{bmatrix}1&3\\ 0&1\end{bmatrix}$ and $ B = \begin{bmatrix}1&-1\\ 0&1\end{bmatrix}$ is given by
The matrix 'X' in the equation $AX = B$, such that $A = \begin{bmatrix}1&3\\ 0&1\end{bmatrix}$ and $ B = \begin{bmatrix}1&-1\\ 0&1\end{bmatrix}$ is given by
Updated On: Jul 2, 2022
- $\begin{bmatrix}1&0\\ -3&1\end{bmatrix}$
- $\begin{bmatrix}1& -4 \\ 0 & 1\end{bmatrix}$
- $\begin{bmatrix}1& -3 \\ 0 &1\end{bmatrix}$
- $\begin{bmatrix} 0 & -1 \\ -3&1\end{bmatrix}$
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The Correct Option is B
Solution and Explanation
Given $A = \begin{bmatrix}1&3\\ 0&1\end{bmatrix} \Rightarrow det A = 1 \ne 0.$
So, $ A^{-1} $ exists. Hence $AX = B$
$ \Rightarrow X = A^{-1} B $
$\Rightarrow X = \begin{bmatrix}1&-3\\ 0&1\end{bmatrix}\begin{bmatrix}1&-1\\ 0&1\end{bmatrix} = \begin{bmatrix}1&-4\\ 0&1\end{bmatrix} $
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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.