Question

If A = \left[\begin{array}{ccc}0&1&2\\2&3&4\\4&5&-6\end{array}\right] [/tex] and [tex] B = \left[\begin{array}{ccc}-1&2&3\\0&1&0\\0&0&-1\end{array}\right] find B - A and 4A - 5B.

Answer 1

Answer:

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

$4A-5B=\left[\begin{array}{ccc}5&-6&-7\\8&7&16\\16&20&-19\end{array}\right]$

Step-by-step explanation:

If

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

and

$B = \left[\begin{array}{ccc}-1&2&3\\0&1&0\\0&0&-1\end{array}\right]$

To find B-A:

$B - A =\left[\begin{array}{ccc}-1&2&3\\0&1&0\\0&0&-1\end{array}\right] -\left[\begin{array}{ccc}0&1&2\\2&3&4\\4&5&-6\end{array}\right] \\\\\\=\left[\begin{array}{ccc}-1-0&2-1&3-2\\0-2&1-3&0-4\\0-4&0-5&-1+6\end{array}\right]\\\\\\B-A=\left[\begin{array}{ccc}-1&1&1\\-2&-2&-4\\-4&-5&5\end{array}\right]$

To find 4A-5B:

$4A-5B =4\left[\begin{array}{ccc}0&1&2\\2&3&4\\4&5&-6\end{array}\right]-5\left[\begin{array}{ccc}-1&2&3\\0&1&0\\0&0&-1\end{array}\right]\\\\\\=\left[\begin{array}{ccc}0&4&8\\8&12&16\\16&20&-24\end{array}\right]-\left[\begin{array}{ccc}-5&10&15\\0&5&0\\0&0&-5\end{array}\right]\\\\\\=\left[\begin{array}{ccc}0+5&4-10&8-15\\8-0&12-5&16-0\\16-0&20-0&-24+5\end{array}\right]\\\\\\4A-5B=\left[\begin{array}{ccc}5&-6&-7\\8&7&16\\16&20&-19\end{array}\right]$