Rui Baldwin

2021-02-24

The product of matrix B and C is matrix D
$\left[\begin{array}{ccc}2& -1& 4\\ g& 0& 3\\ 2& h& 0\end{array}\right]×\left[\begin{array}{cc}-1& 5\\ 4& f\\ -3& 1\end{array}\right]=\left[\begin{array}{cc}i& 24\\ -16& -4\\ 4& e\end{array}\right]$
3.From the expression above, what should be the value of e?
4.From the expression above, what should be the value of g?
5.From the expression above, what should be the value of f?

rogreenhoxa8

Step 1 We are given the two matrices namely
Using the basic rules of multiplication, we have
$B×C=2\left[\begin{array}{ccc}2& -1& 4\\ g& 0& 3\\ 2& h& 0\end{array}\right]×\left[\begin{array}{cc}-1& 5\\ 4& f\\ -3& 1\end{array}\right]$
$⇒B×C=\left[\begin{array}{ccc}4& -2& 8\\ 2g& 0& 6\\ 4& 4h& 0\end{array}\right]×\left[\begin{array}{cc}-1& 5\\ 4& f\\ -3& 1\end{array}\right]$
$⇒B×C=\left[\begin{array}{cc}-4-8-24& 20-2f+8\\ -2g+0-18& 10g+6\\ -4+8h+0& 20+2hf+0\end{array}\right]$
Step 2
Now, we have $B×C=\left[\begin{array}{cc}-4-8-24& 20-2f+8\\ -2g+0-18& 10g+6\\ -4+8h+0& 20+2hf+0\end{array}\right]$ . We are also given that $B×C=\left[\begin{array}{cc}i& 24\\ -16& -4\\ 4& e\end{array}\right]$
Therefore, we now have
$B×C=\left[\begin{array}{cc}-4-8-24& 20-2f+8\\ -2g+0-18& 10g+6\\ -4+8h+0& 20+2hf+0\end{array}\right]=\left[\begin{array}{cc}i& 24\\ -16& -4\\ 4& e\end{array}\right]$. Comparing the entries of the matrices, we have
-36=i, 28-2f=24
2g+18=16,10g+6=-4
8h-4=4,20+2hf=e
Solving these equations, we get
i=-36,f=2,g=-1,h=1,e=24
Step 3
(3). Answer: The value of e is 24.
(4). Answer: The value of g is -1.
(5). Answer: The value of f is 2.

Jeffrey Jordon