If x begin{bmatrix} 2 3 end{bmatrix} + y beg | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the matrix equation: $x \begin{bmatrix} 2 \ 3 \end{bmatrix} + y \begin{bmatrix} -1 \ 1 \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatri

Vedclass · Accepted Answer

$x=3, y=-4$

Vedclass · Answer

(A) Given the matrix equation: $x \begin{bmatrix} 2 \ 3 \end{bmatrix} + y \begin{bmatrix} -1 \ 1 \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatrix}$ Multiplying the scalars $x$ and $y$ into the matrices,we get: $\begin{bmatrix} 2x \ 3x \end{bmatrix} + \begin{bmatrix} -y \ y \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatrix}$ Adding the matrices on the left side: $\begin{bmatrix} 2x - y \ 3x + y \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatrix}$ By comparing the corresponding elements,we obtain a system of linear equations: $1) \ 2x - y = 10$ $2) \ 3x + y = 5$ Adding equation $(1)$ and $(2)$: $(2x - y) + (3x + y) = 10 + 5$ $5x = 15$ $x = 3$ Substituting $x = 3$ into equation $(2)$: $3(3) + y = 5$ $9 + y = 5$ $y = 5 - 9$ $y = -4$ Thus,the values are $x = 3$ and $y = -4$.

If $x \begin{bmatrix} 2 \\ 3 \end{bmatrix} + y \begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix}$,find the values of $x$ and $y$.

Similar Questions

If $\begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = 0$,then $2x + 9 =$ . . . . . .

Express the following matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{ccc}3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2\end{array}\right]$

Assume $X, Y, Z, W$ and $P$ are matrices of order $2 \times n, 3 \times k, 2 \times p, n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7X - 5Z$ is

If $A$ is a $3 \times 4$ matrix and $B$ is a matrix such that $A^{\prime}B$ and $BA^{\prime}$ are both defined,then $B$ is of the type:

If $P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$,$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $Q = PAP^T$,then find $P^T Q^{2015} P$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module