Answer:
[tex]3B - 4C = \left[\begin{array}{cc}-8 &-23\\1&-15\end{array}\right][/tex]
Explanation:
Given
[tex]B = \left[\begin{array}{cc}8&-5\\-1&3\end{array}\right][/tex]
[tex]C = \left[\begin{array}{cc}8&2\\-1&6\end{array}\right][/tex]
Required
Determine 3B - 4C
If
[tex]B = \left[\begin{array}{cc}8&-5\\-1&3\end{array}\right][/tex]
Then
[tex]3B = 3 * \left[\begin{array}{cc}8&-5\\-1&3\end{array}\right][/tex]
[tex]3B = \left[\begin{array}{cc}24&-15\\-3&9\end{array}\right][/tex]
Similarly,
If
[tex]C = \left[\begin{array}{cc}8&2\\-1&6\end{array}\right][/tex]
Then
[tex]4C = 4 * \left[\begin{array}{cc}8&2\\-1&6\end{array}\right][/tex]
[tex]4C = \left[\begin{array}{cc}32&8\\-4&24\end{array}\right][/tex]
So:
[tex]3B - 4C = \left[\begin{array}{cc}24&-15\\-3&9\end{array}\right] - \left[\begin{array}{cc}32&8\\-4&24\end{array}\right][/tex]
This gives:
[tex]3B - 4C = \left[\begin{array}{cc}24 - 32 &-15-8\\-3-(-4)&9-24\end{array}\right][/tex]
[tex]3B - 4C = \left[\begin{array}{cc}-8 &-23\\1&-15\end{array}\right][/tex]
