Question:

If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to

Updated On: Nov 19, 2024
  • $ \left[ \begin{matrix} 5 & 0 \\ 0 & 4 \\ \end{matrix} \right] $
  • $ \left[ \begin{matrix} 7 & 0 \\ 1 & 5 \\ \end{matrix} \right] $
  • $ \left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right] $
  • $ \left[ \begin{matrix} 7 & 1 \\ 0 & 4 \\ \end{matrix} \right] $
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The Correct Option is C

Solution and Explanation

Given, $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ ?.. (i) and
$ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ ..(ii)
On adding both equation, we get
$ 2X=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]+\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\ 2 & 8 \\ \end{matrix} \right] $
$ \Rightarrow $ $ X=\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right] $
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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:

  1. 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.
  2. Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
  3. 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. 
  4. 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. 
  5. Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.