Question

Matrix multiplication problem will fan & medal

Answer 1

.

Answer 2

what have you tried

Answer 3

I tried plugging the numbers into the equation next to it but I'm pretty sure that's incorrect

Answer 4

did you multiply the first matrix by 2?

Answer 5

yes

Answer 6

Assume you have arbitrary entries in your matrix \(X\), say:

\[ X=\left[ \begin{array}{ccc}
a & b \\
d & e \\
\end{array} \right]\]
Then, you have
\[ 2\left[ \begin{array}{ccc}
a & b \\
c & d \\
\end{array} \right]+
2\left[ \begin{array}{ccc}
2 & -8 \\
-4 & 2 \\
\end{array} \right]=
\left[ \begin{array}{ccc}
2a &2b \\
2c & 2d \\
\end{array} \right]+
\left[ \begin{array}{ccc}
4 & -16 \\
-8 & 4 \\
\end{array} \right]=
\left[ \begin{array}{ccc}
2a+4 & 2b-16 \\
2c-8 & 2d+4 \\
\end{array} \right]\]
Now, you need this last matrix to equal the one given in the problem, that is
\[\left[ \begin{array}{ccc}
2a+4 & 2b-16 \\
2c-8 & 2d+4 \\
\end{array} \right]=\left[ \begin{array}{ccc}
4 & -6 \\
2 & -8 \\
\end{array} \right]\]
Thus, you compare entry by entry and solve for \(a,b,c\) and \(d\)
\(2a+4=4\\
2b-16=-6\\
2c-8=2\\
2d+4=-8\)

Answer 7

\[\left[\begin{matrix}0 & 5 \\ 5 & -6\end{matrix}\right]\] is that right?

Answer 8

yes!

Answer 9

thank you!