Given $A = \left[ \begin{array} { c c }
- 9 & 8 \
- 6 & - 5 \
10 & - 16
\end{array} \right]$ and $B = \left[ \begin{array} { l l }
1 & 0 \
2 & 3 \
0 & 4
\end{array} \right]$
, solve $2 X - A = 3 B$
, for $X$
A) $X = \left[ \begin{array} { l l l }
- 3 & 4 & 0 \
5 & 2 & 2
\end{array} \right]$
B) $X = \left[ \begin{array} { l l }
5 & 4 \
0 & 1 \
2 & 2
\end{array} \right]$
C) $X = \left[ \begin{array} { l l }
5 & \frac { 1 } { 2 } \
0 & 2 \
5 & 2
\end{array} \right]$
D) $X = \left[ \begin{array} { c c }
- 3 & 4 \
0 & 2 \
5 & - 2
\end{array} \right]$
E) none

Question

Given $A = \left[ \begin{array} { c c } 
- 9 & 8 \
- 6 & - 5 \
10 & - 16
\end{array} \right]$ and $B = \left[ \begin{array} { l l } 
1 & 0 \
2 & 3 \
0 & 4
\end{array} \right]$
, solve $2 X - A = 3 B$
, for $X$
A) $X = \left[ \begin{array} { l l l } 
- 3 & 4 & 0 \
5 & 2 & 2
\end{array} \right]$
B) $X = \left[ \begin{array} { l l } 
5 & 4 \
0 & 1 \
2 & 2
\end{array} \right]$
C) $X = \left[ \begin{array} { l l } 
5 & \frac { 1 } { 2 } \
0 & 2 \
5 & 2
\end{array} \right]$
D) $X = \left[ \begin{array} { c c } 
- 3 & 4 \
0 & 2 \
5 & - 2
\end{array} \right]$
E) none

Quizplus · Accepted Answer

We can start by rearranging the given equation to solve for X as follows:

\begin{align*}
2X - A &= 3B \
2X &= 3B + A \
X &= \frac{3}{2}B + \frac{1}{2}A
\end{align*}

We can now substitute the given matrices for A and B and perform the required scalar multiplication and matrix addition. The resulting matrix X should match one of the choices given:

\begin{align*}
X &= \frac{3}{2} \begin{bmatrix}
1 & 0 \
2 & 3 \
0 & 4
\end{bmatrix}
+ \frac{1}{2} \begin{bmatrix}
-9 & 8 \
-6 & -5 \
10 & -16
\end{bmatrix} \
&= \begin{bmatrix}
\frac{3}{2}(1) + \frac{1}{2}(-9) & \frac{3}{2}(0) + \frac{1}{2}(8) \
\frac{3}{2}(2) + \frac{1}{2}(-6) & \frac{3}{2}(3) + \frac{1}{2}(-5) \
\frac{3}{2}(0) + \frac{1}{2}(10) & \frac{3}{2}(4) + \frac{1}{2}(-16)
\end{bmatrix} \
&= \begin{bmatrix}
-3 & 4 \
0 & 2 \
5 & -2
\end{bmatrix}
\end{align*}

Therefore, the best choice is D.

Given A=[−98−6−510−16]A = \left[ \begin{array} { c c } - 9 & 8 \\- 6 & - 5 \\10 & - 16\end{array} \right]A=​−9−610​8−5−16​​

Given $A = \left[ \begin{array} { c c } - 9 & 8 \\- 6 & - 5 \\10 & - 16\end{array} \right]$