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 ar

1 thought on “Find A and B if 2A + 3B = (1 −2 3 2 0 −1)& A – 2B = (3 0 1 −1 6 2)<br /> ( The matrices are of order 2 x 3 and the elements ar”

1. Given :

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

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

   To Find : A and B

   Solution:

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

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

   2 * Eq1 + 3 * Eq2

   LHS = 4A + 6B + 3A – 6B = 7A

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

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

   Similarly solve for B

   Eq1 – 2 * Eq2

   LHS = 2A + 3B – 2A + 4B = 7B

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

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

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