Solve the matrix equation for X.
-Let $A = \left[ \begin{array} { r r } 3 & - 3 \ - 4 & 0 \ 4 & - 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 4 & 0 \ 0 & - 2 \ 3 & - 5 \end{array} \right]$
A)
$$X = \left[ \begin{array} { r r }
\frac { 1 } { 4 } & \frac { 3 } { 4 } \
1 & - \frac { 1 } { 2 } \
- \frac { 1 } { 4 } & 0
\end{array} \right]$$
B)
$$X = \left[ \begin{array} { r r }
- \frac { 1 } { 4 } & - \frac { 3 } { 4 } \
- 1 & \frac { 1 } { 2 } \
\frac { 1 } { 4 } & 0
\end{array} \right]$$
C)
$X=\left[\begin{array}{rr}
1 & 3 \
4 & -2 \
-1 & 0
\end{array}\right]$

D)
$X=\left[\begin{array}{rr}
-1 & 3 \
-4 & 2 \
1 & 0
\end{array}\right]$

Question

Solve the matrix equation for X.
-Let $A = \left[ \begin{array} { r r } 3 & - 3 \ - 4 & 0 \ 4 & - 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 4 & 0 \ 0 & - 2 \ 3 & - 5 \end{array} \right]$
A)
$$X = \left[ \begin{array} { r r } 
\frac { 1 } { 4 } & \frac { 3 } { 4 } \
1 & - \frac { 1 } { 2 } \
- \frac { 1 } { 4 } & 0
\end{array} \right]$$
B)
$$X = \left[ \begin{array} { r r } 
- \frac { 1 } { 4 } & - \frac { 3 } { 4 } \
- 1 & \frac { 1 } { 2 } \
\frac { 1 } { 4 } & 0
\end{array} \right]$$
C)
$X=\left[\begin{array}{rr}
1 & 3 \
4 & -2 \
-1 & 0
\end{array}\right]$

D) 
$X=\left[\begin{array}{rr}
-1 & 3 \
-4 & 2 \
1 & 0
\end{array}\right]$

Quizplus · Accepted Answer

The matrix equation we need to solve is of the form AX = B.
So we need to find X, therefore the solution is X = A^(-1)B.
First we need to find the inverse of matrix A, which is:
$$A^{-1} = \left[ \begin{array} { r r } 
\frac{5}{12} & \frac{3}{8} & \frac{1}{4} \
\frac{2}{3} & \frac{1}{2} & \frac{1}{2} \
\frac{5}{12} & \frac{5}{8} & 0
\end{array} \right]$$
Now we just need to multiply A^(-1) and B to get X:
$$X = A^{-1}B = \left[ \begin{array} { r r } 
\frac { 1 } { 4 } & \frac { 3 } { 4 } \
1 & - \frac { 1 } { 2 } \
- \frac { 1 } { 4 } & 0
\end{array} \right]$$

Solve the Matrix Equation for X A=[3−3−404−5]A = \left[ \begin{array} { r r } 3 & - 3 \\ - 4 & 0 \\ 4 & - 5 \end{array} \right]A=​3−44​−30−5​​

Solve the Matrix Equation for X $A = \left[ \begin{array} { r r } 3 & - 3 \\ - 4 & 0 \\ 4 & - 5 \end{array} \right]$