pedzenekO

2020-12-05

$A=\left[\begin{array}{ccc}1& -3& 3\\ 1& 0& -2\end{array}\right],B=\left[\begin{array}{ccc}-3& 1& 2\\ 2& 5& -3\end{array}\right]$
Find 2B?

Pohanginah

Step 1
Given Matrices A and B -
$A=\left[\begin{array}{ccc}1& -3& 3\\ 1& 0& -2\end{array}\right],B=\left[\begin{array}{ccc}-3& 1& 2\\ 2& 5& -3\end{array}\right]$
2B=?
Rule to multiuply a number with matrices,
Let X be a matrix -
$X=\left[\begin{array}{ccc}a& b& c\\ d& e& f\end{array}\right]$
Multiplying by m in matix X,
$mX=m\left[\begin{array}{ccc}a& b& c\\ d& e& f\end{array}\right]$
$mX=\left[\begin{array}{ccc}m×a& m×b& m×c\\ m×d& m×e& m×f\end{array}\right]$
Hence,
$2B=2\left[\begin{array}{ccc}-3& 1& 2\\ 2& 5& -3\end{array}\right]$
$2B=\left[\begin{array}{ccc}2×\left(-3\right)& 2×\left(1\right)& 2×\left(2\right)\\ 2×\left(2\right)& 2×\left(5\right)& 2×\left(-3\right)\end{array}\right]$
$2B=\left[\begin{array}{ccc}-6& 2& 4\\ 4& 10& -6\end{array}\right]$
Hence,
$2B=\left[\begin{array}{ccc}-6& 2& 4\\ 4& 10& -6\end{array}\right]$

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