Question:
if $A = \begin{bmatrix}4&1&0\\ 1&-2&2\end{bmatrix} , B = \begin{bmatrix}2&0&-1\\ 3&1&x\end{bmatrix} , C = \begin{bmatrix}1\\ 2\\ 1\end{bmatrix}$ and $D =\begin{bmatrix}15+x\\ 1\end{bmatrix}$ such that $(2A -3B)C=D$, then $x$ =
if $A = \begin{bmatrix}4&1&0\\ 1&-2&2\end{bmatrix} , B = \begin{bmatrix}2&0&-1\\ 3&1&x\end{bmatrix} , C = \begin{bmatrix}1\\ 2\\ 1\end{bmatrix}$ and $D =\begin{bmatrix}15+x\\ 1\end{bmatrix}$ such that $(2A -3B)C=D$, then $x$ =
Updated On: Jul 6, 2022
- $3$
- $-4$
- $-6$
- $6$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$(2A - 3B) C =D$
$\Rightarrow\left[2\begin{bmatrix}4&1&0\\ 1&-2&2\end{bmatrix}-3 \begin{bmatrix}2&0&-1\\ 3&1&x\end{bmatrix}\right] \begin{bmatrix}1\\ 2\\ 1\end{bmatrix} =\begin{bmatrix}15+x\\ 1\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2&2&3\\ -7&-7&4-3x\end{bmatrix} \begin{bmatrix}1\\ 2\\ 1\end{bmatrix} =\begin{bmatrix}15+x\\ 1\end{bmatrix}$
$\Rightarrow \begin{bmatrix}9\\ -17-3x\end{bmatrix} = \begin{bmatrix}15+x\\ 1\end{bmatrix} \Rightarrow x = -6$
Was this answer helpful?
0
0
Top Questions on Matrices
- If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:
- Which of the following statements is not correct?
- If A and B are two matrices such that AB is an identity matrix and the order of matrix B is \(3 \times 4\), then the order of matrix A is:
- If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:
- If \( B = \begin{bmatrix} 1 & 3 \\ 2 & \alpha \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( |A| = 2 \), then the value of \( \alpha \) is:
View More Questions
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.