Answer:
[tex]c_{24}[/tex] is -12
[tex]d_{13}[/tex] is 14
Step-by-step explanation:
To find 2A multiply each element in A by 2
To find 3B multiply each element in B by 3
∵ [tex]A=\left[\begin{array}{cccc}-3&1&0&5\\5&-6&1&3\\8&2&6&-5\end{array}\right][/tex]
- Multiply it by 2
∴ [tex]2A=\left[\begin{array}{cccc}-6&2&0&10\\10&-12&2&6\\16&4&12&-10\end{array}\right][/tex]
∵ [tex]B=\left[\begin{array}{cccc}5&3&-7&-5\\0&1&6&-6\\5&-4&9&3\end{array}\right][/tex]
- Multiply it by 3
∴ [tex]3B=\left[\begin{array}{cccc}15&9&-21&-15\\0&3&18&-18\\15&-12&27&9\end{array}\right][/tex]
Now lets find C
∵ C = 2A + 3B
- Add each two corresponding elements in 2A and 3B
∴ [tex]C=2A+3B=\left[\begin{array}{cccc}9&11&-21&-5\\10&-9&20&-12\\31&-8&39&-1\end{array}\right][/tex]
∵ [tex]c_{24}[/tex] means element in 2nd row and 4th column
- The element in the 2nd row and 4th column is -12
∴ [tex]c_{24}[/tex] is -12
∵ D = 3A - 2B
- Multiply A by 3 and B by 2, then subtract every elements in 2B
from the corresponding element in 3A
∵ [tex]3A=\left[\begin{array}{cccc}-9&3&0&15\\15&-18&3&9\\24&6&12&-15\end{array}\right][/tex]
∵ [tex]2B=\left[\begin{array}{cccc}10&6&-14&-10\\0&2&12&-12\\10&-8&18&6\end{array}\right][/tex]
∴ [tex]D=3A-2B=\left[\begin{array}{cccc}-19&-3&14&25\\15&-20&-9&21\\14&14&-6&-21\end{array}\right][/tex]
∵ [tex]d_{13}[/tex] means element in 1st row and 3rd column
- The element in the 1st row and 3rd column is 14
∴ [tex]d_{13}[/tex] is 14
