nagasenaz

2021-02-25

Use the matrices AA and BB below instead of those in your text.
$A=\left[\begin{array}{cc}-6& -1\\ -3& -4\end{array}\right]B=\left[\begin{array}{cc}-1& 3\\ -5& -8\end{array}\right]$ 1) 2A+B=? 2)A-4B=?

likvau

Step 1
To determine the values of the given matrix expressions (as matrices)
Step 2
Matrix addition (substraction) , scalar multiplication are performed entriwise
Step 3
Matrix addition, (subtraction) and scalar multiplication rules
If $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right],B=\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]$ then
$A±B=\left[\begin{array}{cc}a±p& b±q\\ c±r& d±s\end{array}\right]$ and
$kA=\left[\begin{array}{cc}ka& kb\\ kc& kd\end{array}\right]$ (k any scalar)
Step 4
1) computing 2A+B
$2A+B=\left[\begin{array}{cc}-12& -2\\ -6& -8\end{array}\right]+\left[\begin{array}{cc}-1& 3\\ -5& -8\end{array}\right]$
$=\left[\begin{array}{cc}-12-1& -2+3\\ -6-5& -8-8\end{array}\right]$
$=\left[\begin{array}{cc}-13& 1\\ -11& -16\end{array}\right]$
step 5
2) Computing A-4B
$A-4B=\left[\begin{array}{cc}-6& -1\\ -3& -4\end{array}\right]+\left[\begin{array}{cc}4& -12\\ 20& 32\end{array}\right]$
$=\left[\begin{array}{cc}-2& -13\\ 17& 28\end{array}\right]$

Jeffrey Jordon

Answer is given below (on video)

Jeffrey Jordon