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

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(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]

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(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

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