Question:
If $\begin{pmatrix}2x+y&x+y\\ p-q&p+q\end{pmatrix}=\begin{pmatrix}1&1\\ 0&0\end{pmatrix}$ , then $(x, y, p, q) $ equals
If $\begin{pmatrix}2x+y&x+y\\ p-q&p+q\end{pmatrix}=\begin{pmatrix}1&1\\ 0&0\end{pmatrix}$ , then $(x, y, p, q) $ equals
Updated On: Jun 7, 2024
- 0, 1, 0, 0
- 0, -1, 0, 0
- 1, 0, 0, 0
- 0, 1, 0, 1
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The Correct Option is A
Solution and Explanation
We have,
$\begin{bmatrix}2 x+y & x+y \\ p-q & p+q\end{bmatrix}=\begin{bmatrix}1 & 1 \\ 0 & 0\end{bmatrix}$
$\therefore \,\, 2 x+y=1 \,\,\,...(i)$
$x+y=1\,\,\,...(ii)$
$p-q=0\,\,\,...(iii)$
$p+q=0\,\,\,...(iv)$
On solving Eqs. (i) and (ii), we get
$x=0, y=1$
and on solving Eqs. (iii) and (iv), we get
$p=q=0$
$\begin{bmatrix}2 x+y & x+y \\ p-q & p+q\end{bmatrix}=\begin{bmatrix}1 & 1 \\ 0 & 0\end{bmatrix}$
$\therefore \,\, 2 x+y=1 \,\,\,...(i)$
$x+y=1\,\,\,...(ii)$
$p-q=0\,\,\,...(iii)$
$p+q=0\,\,\,...(iv)$
On solving Eqs. (i) and (ii), we get
$x=0, y=1$
and on solving Eqs. (iii) and (iv), we get
$p=q=0$
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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.