Question

Find A and B if 2A + 3B = (1 −2 3 2 0 −1)& A - 2B = (3 0 1 −1 6 2)
( The matrices are of order 2 x 3 and the elements are written row wise)

Answer 1

Given :

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

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

To Find : A and B

Solution:

$2A+3B=\left[\begin{array}{ccc}1&-2&3\\2&0&-1\end{array}\right]$   Eq1

$A-2B=\left[\begin{array}{ccc}3&0&1\\-1&6&2\end{array}\right]$        Eq2

2 * Eq1  + 3 * Eq2

LHS  = 4A + 6B + 3A - 6B  = 7A

$7A=\left[\begin{array}{ccc}11&-4&9\\1&18&4\end{array}\right]$  

$A=\left[\begin{array}{ccc}11/7&-4/7&9/7\\1/7&18/7&4/7\end{array}\right]$  

Similarly solve for B

Eq1 - 2 * Eq2

LHS = 2A + 3B  - 2A  + 4B  = 7B

$7B=\left[\begin{array}{ccc}-5&-2&1\\4&-12&-5\end{array}\right]$  

$B=\left[\begin{array}{ccc}-5/7&-2/7&1/7\\4/7&-12/7&-5/7\end{array}\right]$

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