6)
a)
[tex]\left[\begin{array}{cc}2&3\\-1&4\end{array}\right]+\left[\begin{array}{cc}5&2\\-2&0\end{array}\right] =\left[\begin{array}{cc}2+5&3+2\\-1+(-2)&4+0\end{array}\right] =\boxed{\left[\begin{array}{cc}7&5\\-3&4\end{array}\right] }[/tex]
b)
[tex]5\left[\begin{array}{ccc}5&-6\\-1&5\\0&1\end{array}\right] =\left[\begin{array}{ccc}5(5)&5(-6)\\5(-1)&5(5)\\5(0)&5(1)\end{array}\right] =\boxed{\left[\begin{array}{ccc}25&-30\\-5&25\\0&5\end{array}\right] }[/tex]
c)
[tex]\left[\begin{array}{ccc}-5&0&7\\2&3&2\end{array}\right] -\left[\begin{array}{ccc}-5&2&5\\1&-3&4\end{array}\right] =[/tex]
[tex]\left[\begin{array}{ccc}-5-(-5)&0-2&7-5\\2-1&3-(-3)&2-4\end{array}\right] =\boxed{\left[\begin{array}{ccc}0&-2&2\\1&6&-2\end{array}\right] }[/tex]
7)
a)
[tex]\left[\begin{array}{c}4\end{array}\right] \ \to\ \det{\left[\begin{array}{c}4\end{array}\right]}=\boxed{4}[/tex]
b)
[tex]\left[\begin{array}{cc}-2&0\\5&3\end{array}\right] \ \to\ \det{\left[\begin{array}{cc}-2&0\\5&3\end{array}\right]}=-2(3)-0(5)=\boxed{-6}[/tex]
c)
[tex]\left[\begin{array}{ccc}2&3&1\\0&-3&5\\1&2&3\end{array}\right] \ \to\ \det{\left[\begin{array}{ccc}2&3&1\\0&-3&5\\1&2&3\end{array}\right]}=[/tex]
[tex]2(-3)(3)+3(5)(1)-1(-3)(1)-2(5)(2)=\boxed{-20}[/tex]
