If m[-3, 4] + n[4, -3] = [10, -11], then 3m + | vedclass

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

Question

(D) Given the matrix equation: $m[-3, 4] + n[4, -3] = [10, -11]$ Multiplying the scalars $m$ and $n$ into the matrices, we get: $[-3m, 4m] + [4n, -3n]

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Given the matrix equation: $m[-3, 4] + n[4, -3] = [10, -11]$ Multiplying the scalars $m$ and $n$ into the matrices, we get: $[-3m, 4m] + [4n, -3n] = [10, -11]$ Adding the matrices, we have: $[-3m + 4n, 4m - 3n] = [10, -11]$ By equating the corresponding elements, we obtain two linear equations: $-3m + 4n = 10$ $\dots(i)$ $4m - 3n = -11$ $\dots(ii)$ To solve for $m$ and $n$, multiply equation $(i)$ by $3$ and equation $(ii)$ by $4$: $-9m + 12n = 30$ $\dots(iii)$ $16m - 12n = -44$ $\dots(iv)$ Adding equations $(iii)$ and $(iv)$: $7m = -14 \Rightarrow m = -2$ Substituting $m = -2$ into equation $(i)$: $-3(-2) + 4n = 10 \Rightarrow 6 + 4n = 10 \Rightarrow 4n = 4 \Rightarrow n = 1$ Finally, calculating $3m + 7n$: $3(-2) + 7(1) = -6 + 7 = 1$

If $m[-3, 4] + n[4, -3] = [10, -11]$, then $3m + 7n$ is equal to

Similar Questions

The matrix $A = \frac{1}{3}\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ -2 & 2 & -1 \end{bmatrix}$ is

Which of the given values of $x$ and $y$ make the following pair of matrices equal?
$\left[\begin{array}{cc}3x+7 & 5 \\ y+1 & 2-3x\end{array}\right]=\left[\begin{array}{cc}0 & y-2 \\ 8 & 4\end{array}\right]$

Which of the following matrices can $NOT$ be obtained from the matrix $\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$ by a single elementary row operation?

If $P = \begin{bmatrix} 1 & 0 \\ 1/2 & 1 \end{bmatrix}$,then $P^{50}$ is:

Compute the indicated product: $\begin{bmatrix} a & b \\ -b & a \end{bmatrix} \begin{bmatrix} a & -b \\ b & a \end{bmatrix}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module