Question

If A = $\left[\begin{array}{ccc}1&5&3\\2&4&0\\3&-1&-5\end{array}\right]$ and B = $\left[\begin{array}{ccc}2&-1&0\\0&-2&5\\1&2&0\end{array}\right]$ then find 3A' - 4B'.

Answer 1

Answer:

See the attachment.

Step-by-step explanation:

In the attachment I have answered this problem.

See the attachment for detailed solution.

I hope this answer helps you

Answer 2

As we know that transpose of a matrix is given as interchange of rows with columns

If A = $\left[\begin{array}{ccc}1&5&3\\2&4&0\\3&-1&-5\end{array}\right]$

A' = $\left[\begin{array}{ccc}1&2&3\\5&4&-1\\3&0&-5\end{array}\right]$
3A' = $\left[\begin{array}{ccc}3&6&9\\15&12&-3\\9&0&-15\end{array}\right]$

B = $\left[\begin{array}{ccc}2&-1&0\\0&-2&5\\1&2&0\end{array}\right]$

B' = $\left[\begin{array}{ccc}2&0&1\\-1&-2&2\\0&5&0\end{array}\right]$

4B' = $\left[\begin{array}{ccc}8&0&4\\-4&-8&8\\0&20&0\end{array}\right]$

3A' - 4B'=$\left[\begin{array}{ccc}3&6&9\\15&12&-3\\9&0&-15\end{array}\right]$+$\left[\begin{array}{ccc}-8&0&-4\\4&8&-8\\0&-20&0\end{array}\right]$

=$\left[\begin{array}{ccc}3-8&6&9-4\\15+4&12+8&-3-8\\9&0-20&-15\end{array}\right]$

3A'-4B'=$\left[\begin{array}{ccc}-5&6&5\\19&20&-11\\9&-20&-15\end{array}\right]$