djeljenike

2021-01-02

Given the matrices

Determine the following
i)2A-B+2C ii)A+B+C iii)4C-2B+3A iv)$\left(A×B\right)-C$

Macsen Nixon

Step 1
To find the following from the given matrices A,B and C.
Step 2
Given that

(i)2A-B+2C
$2\left[\begin{array}{ccc}1& -1& 2\\ 3& 4& 5\\ 0& 1& -1\end{array}\right]-\left[\begin{array}{ccc}0& 2& 1\\ 3& 0& 5\\ 7& -6& 0\end{array}\right]+2\left[\begin{array}{ccc}0& 0& 2\\ 3& 1& 0\\ 0& -2& 4\end{array}\right]$
$=\left[\begin{array}{ccc}2& -2& 4\\ 6& 8& 10\\ 0& 2& -2\end{array}\right]-\left[\begin{array}{ccc}0& 2& 1\\ 3& 0& 5\\ 7& -6& 0\end{array}\right]+\left[\begin{array}{ccc}0& 0& 4\\ 6& 2& 0\\ 0& -4& 8\end{array}\right]$
$=\left[\begin{array}{ccc}2-0+0& -2-2+0& 4-1+4\\ 6-3+6& 8-0+2& 10-5+0\\ 0-7+0& 2+6-4& -2-0+8\end{array}\right]$
$=\left[\begin{array}{ccc}2& -4& 7\\ 9& 10& 5\\ -7& 4& 6\end{array}\right]$
$\therefore 2A-B+2C=\left[\begin{array}{ccc}2& -4& 7\\ 9& 10& 5\\ -7& 4& 6\end{array}\right]$
(ii)A+B+C
$=\left[\begin{array}{ccc}1& -1& 2\\ 3& 4& 5\\ 0& 1& -1\end{array}\right]+\left[\begin{array}{ccc}0& 2& 1\\ 3& 0& 5\\ 7& -6& 0\end{array}\right]+\left[\begin{array}{ccc}0& 0& 2\\ 3& 1& 0\\ 0& -2& 4\end{array}\right]$
$=\left[\begin{array}{ccc}1+0+0& -1+2+0& 2+1+2\\ 3+3+3& 4+0+1& 5+5+0\\ 0+7+0& 1-6-2& -1+0+4\end{array}\right]$
$=\left[\begin{array}{ccc}1& 1& 5\\ 9& 5& 10\\ 7& -7& 3\end{array}\right]\therefore A+B+C=\left[\begin{array}{ccc}1& 1& 5\\ 9& 5& 10\\ 7& -7& 3\end{array}\right]$
(iii)4C-2B+3A

Jeffrey Jordon