CoormaBak9

2020-12-16

Compute the following
a) $\left[\begin{array}{cccccc}-5& -4& 3& -10& -3& 6\\ 6& -10& 5& 9& 4& -1\end{array}\right]+\left[\begin{array}{cccccc}-7& 3& 10& 0& 8& 8\\ 8& 0& 4& -3& -8& 0\end{array}\right]$
b) $-5\left[\begin{array}{ccc}8& -10& 7\\ 0& -9& 7\\ 10& -5& -10\\ 1& 5& -10\end{array}\right]$
c)${\left[\begin{array}{ccc}3& 0& -8\\ 6& -4& -2\\ 6& 0& -8\\ -9& -7& -7\end{array}\right]}^{T}$

### Answer & Explanation

Gennenzip

Part (a)
Given:
$\left[\begin{array}{cccccc}-5& -4& 3& -10& -3& 6\\ 6& -10& 5& 9& 4& -1\end{array}\right]+\left[\begin{array}{cccccc}-7& 3& 10& 0& 8& 8\\ 8& 0& 4& -3& -8& 0\end{array}\right]$
By using matrix addition
$\left[\begin{array}{cccccc}-5& -4& 3& -10& -3& 6\\ 6& -10& 5& 9& 4& -1\end{array}\right]+\left[\begin{array}{cccccc}-7& 3& 10& 0& 8& 8\\ 8& 0& 4& -3& -8& 0\end{array}\right]$
$=\left[\begin{array}{cccccc}-5+\left(-7\right)& -4+3& 3+10& -10+0& -3+8& 6+8\\ 6+8& -10+0& 5+4& 9+\left(-3\right)& 4+\left(-8\right)& -1+0\end{array}\right]$
$\left[\begin{array}{cccccc}-12& -1& 13& -10& 5& 14\\ 14& -10& 9& 6& -4& -1\end{array}\right]$
Part (b)
Given:
$-5\left[\begin{array}{ccc}8& -10& 7\\ 0& -9& 7\\ 10& -5& -10\\ 1& 5& -10\end{array}\right]$
Using scalar multiplication of matrices.
$-5\left[\begin{array}{ccc}8& -10& 7\\ 0& -9& 7\\ 10& -5& -10\\ 1& 5& -10\end{array}\right]=\left[\begin{array}{ccc}-5\left(8\right)& -5\left(-10\right)& -5\left(7\right)\\ -5\left(0\right)& -5\left(-9\right)& -5\left(7\right)\\ -5\left(10\right)& -5\left(-5\right)& -5\left(-10\right)\\ -5\left(1\right)& -5\left(5\right)& -5\left(-10\right)\end{array}\right]$
$\left[\begin{array}{ccc}-40& 50& -35\\ 0& 45& -35\\ -50& 25& 50\\ -5& -25& 50\end{array}\right]$
Part (c)
Given:
${\left[\begin{array}{ccc}3& 0& -8\\ 6& -4& -2\\ 6& 0& -8\\ -9& -7& -7\end{array}\right]}^{T}$
Transpose of a matrix is obtained by flipping matrix along diagonal,
${\left[\begin{array}{ccc}3& 0& -8\\ 6& -4& -2\\ 6& 0& -8\\ -9& -7& -7\end{array}\right]}^{T}=\left[\begin{array}{cccc}3& 6& 6& -9\\ 0& -4& 0& -7\\ -8& -2& -8& -7\end{array}\right]$

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