Exercise 74 Page 288

We can see that the given matrices have the same dimensions, $2\times 2.$ Multiplication by a scalar does not affect the dimension of a matrix, so it is possible to perform the addition and subtraction of the given matrices after multiplying them by scalars. We will start with the scalar multiplication.

$\text{-}2\left[\begin{array}{cc}5& \text{-}9\\ 5& 11\end{array}\right]-6\left[\begin{array}{cc}3& \text{-}7\\ \text{-}5& 8\end{array}\right]$

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Multiply matrices by scalars

Multiply matrix by $\text{-}2$

$\left[\begin{array}{cc}(\text{-}2)(5)& (\text{-}2)(\text{-}9)\\ (\text{-}2)(5)& (\text{-}2)(11)\end{array}\right]-6\left[\begin{array}{cc}3& \text{-}7\\ \text{-}5& 8\end{array}\right]$

Multiply matrix by $6$

$\left[\begin{array}{cc}(\text{-}2)(5)& (\text{-}2)(\text{-}9)\\ (\text{-}2)(5)& (\text{-}2)(11)\end{array}\right]-\left[\begin{array}{cc}(6)(3)& (6)(\text{-}7)\\ (6)(\text{-}5)& (6)(8)\end{array}\right]$

Multiply

Multiply

$\left[\begin{array}{cc}\text{-}10& 18\\ \text{-}10& \text{-}22\end{array}\right]-\left[\begin{array}{cc}18& \text{-}42\\ \text{-}30& 48\end{array}\right]$

Subtract matrices

$\left[\begin{array}{cc}\text{-}10-18& 18-(\text{-}42)\\ \text{-}10-(\text{-}30)& \text{-}22-48\end{array}\right]$

AddSubTerms

Add and subtract terms

$\left[\begin{array}{cc}\text{-}28& 60\\ 20& \text{-}70\end{array}\right]$