Solve the matrix equation for X.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 5 & 1 & - 4 \ 5 & 0 & 0 \ 1 & - 5 & 4 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } - 1 & - 5 & - 4 \ 0 & 1 & 1 \ 5 & 0 & 5 \end{array} \right] ; \quad 4 \mathrm {~B} - 4 \mathrm {~A} = \mathrm { X }$
A)
$$X = \left[ \begin{array} { r r r }
- 24 & - 24 & 0 \
- 20 & 4 & 4 \
16 & 20 & 4
\end{array} \right]$$
B)
$X = \left[ \begin{array} { r r r } - 20 & 4 & 4 \ 16 & 20 & 4 \ - 24 & - 24 & 0 \end{array} \right]$
C)
$X = \left[ \begin{array} { r r r } - 24 & - 24 & 0 \ - 20 & 1 & 1 \ 16 & 20 & 4 \end{array} \right]$
D)
$X = \left[ \begin{array} { r r r } - 20 & 1 & 1 \ 16 & 20 & 4 \ - 24 & - 24 & 0 \end{array} \right]$

Question

Solve the matrix equation for X.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 5 & 1 & - 4 \ 5 & 0 & 0 \ 1 & - 5 & 4 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } - 1 & - 5 & - 4 \ 0 & 1 & 1 \ 5 & 0 & 5 \end{array} \right] ; \quad 4 \mathrm {~B} - 4 \mathrm {~A} = \mathrm { X }$
A)
$$X = \left[ \begin{array} { r r r } 
- 24 & - 24 & 0 \
- 20 & 4 & 4 \
16 & 20 & 4
\end{array} \right]$$
B)
$X = \left[ \begin{array} { r r r } - 20 & 4 & 4 \ 16 & 20 & 4 \ - 24 & - 24 & 0 \end{array} \right]$
C)
$X = \left[ \begin{array} { r r r } - 24 & - 24 & 0 \ - 20 & 1 & 1 \ 16 & 20 & 4 \end{array} \right]$
D)
$X = \left[ \begin{array} { r r r } - 20 & 1 & 1 \ 16 & 20 & 4 \ - 24 & - 24 & 0 \end{array} \right]$

Quizplus · Accepted Answer

To solve for $X$, we calculate $4B - 4A$. Multiplying each matrix by 4 and then subtracting $4A$ from $4B$ gives the result:$$4B = \left[ \begin{array} { r r r } -4 & -20 & -16 \ 0 & 4 & 4 \ 20 & 0 & 20 \end{array} \right]$$$$4A = \left[ \begin{array} { r r r } 20 & 4 & -16 \ 20 & 0 & 0 \ 4 & -20 & 16 \end{array} \right]$$Subtracting $4A$ from $4B$ yields:$$\left[ \begin{array} { r r r } -24 & -24 & 0 \ -20 & 4 & 4 \ 16 & 20 & 4 \end{array} \right]$$

Solve the Matrix Equation for X A=[51−45001−54]\mathrm { A } = \left[ \begin{array} { r r r } 5 & 1 & - 4 \\ 5 & 0 & 0 \\ 1 & - 5 & 4 \end{array} \right]A=​551​10−5​−404​​

Solve the Matrix Equation for X $\mathrm { A } = \left[ \begin{array} { r r r } 5 & 1 & - 4 \\ 5 & 0 & 0 \\ 1 & - 5 & 4 \end{array} \right]$