Question:
If $ x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right], $ then
If $ x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right], $ then
Updated On: Jun 23, 2024
- $ x=-2,\,y=1 $
- $ x=-9,y=10 $
- $ x=22,y=1 $
- $ x=2,y=-1 $
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The Correct Option is A
Solution and Explanation
Given that, $ x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right] $
$ \therefore $ $ -3x+4y=10 $ ..(i)
and $ 4x+3y=-5 $ ..(ii)
On multiplying E (i) by 4 and E (ii) by 4 and then subtracting, we get
$ -25x=50 $
$ \Rightarrow $ $ x=-2 $
$ \therefore $ $ -3x+4y=10 $ ..(i)
and $ 4x+3y=-5 $ ..(ii)
On multiplying E (i) by 4 and E (ii) by 4 and then subtracting, we get
$ -25x=50 $
$ \Rightarrow $ $ x=-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.
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