Question

If $A= \left[\begin{array}{ccc}0&-1\\4&-2\end{array}\right], B= \left[\begin{array}{ccc}-5\\6\end{array}\right]$ and 3A × M = 2B, find :
i) The order of matrix M.ii) The value of matrix M.

Answer 1

Answer:

1) Order of Matrix M: [2×1]

2)Value of Matrix M

$M= \left[\begin{array}{ccc}\frac{8}{3}\\\\\frac{10}{3}\end{array}\right]$

Solution:

we know that two matrix can multiply only if column of first matrix are equal to row of second matrix

So

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

So M can be [2×2] and [2×1] for Multiplication

but for equality M can be [2×1]

let

$M= \left[\begin{array}{ccc}x\\y\end{array}\right]$

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

$\left[\begin{array}{ccc}0&-3\\12&-6\end{array}\right] \times \left[\begin{array}{ccc}x\\y\end{array}\right]= \left[\begin{array}{ccc}-10\\12\end{array}\right]$

$\left[\begin{array}{ccc}0-3y\\12x-6y\end{array}\right]= \left[\begin{array}{ccc}-10\\12\end{array}\right]$

$- 3y = - 10 \\ \\ y = \frac{10}{3} \\ \\ 12x - 6y = 12 \\ \\ 12x - 6( \frac{10}{3} ) = 12 \\ \\ 12x - 20 = 12 \\ \\ 12x = 32 \\ \\ x = \frac{8}{3}$

So

$M= \left[\begin{array}{ccc}\frac{8}{3}\\\\\frac{10}{3}\end{array}\right]$

Hope it helps you.