Question

Please solve it in detail. I will mark you as brainliest.

Answer 1

Answer:

$X=\left[\begin{array}{cc}-2&-10/3 \\4&14/3 \\-31/3&-7/3\end{array}\right]$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

$A = \left[\begin{array}{cc}8&0\\4&-2\\3&6\end{array}\right]$

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

2A + 3X = 5B

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The value of x

$\Large{\underline{\underline{\bf{Solution:}}}}$

2A + 3X = 5B

3X = 5B - 2A

X = 1/3[5B - 2A]

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

$5B=\left[\begin{array}{cc}10&-10\\20&10\\-25&5\end{array}\right]$

$2A = 2\left[\begin{array}{cc}8&0\\4&-2\\3&6\end{array}\right]$

$2A=\left[\begin{array}{cc}16&0\\8&-4\\6&12\end{array}\right]$

$5B-2A=\left[\begin{array}{cc}10&-10\\20&10\\-25&5\end{array}\right]-\left[\begin{array}{cc}16&0\\8&-4\\6&12\end{array}\right]$

$5B-2A=\left[\begin{array}{cc}-6&-10\\12&14\\-31&-7\end{array}\right]$

$\dfrac{1}{3} (5B-2A)=\dfrac{1}{3} \left[\begin{array}{cc}-6&-10\\12&14\\-31&-7\end{array}\right]$

$X=\left[\begin{array}{cc}-2&-10/3 \\4&14/3 \\-31/3&-7/3\end{array}\right]$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Matrix multiplication is not commutative. That is if A and B are two matrices, AB $\neq$ BA

→ Matrix multiplication is associative. If A,B,C are three matrices,

 (AB) C = A (BC)

→ Matrix multiplication is distributive. If A,B,C are three matrices,

  A (B+C) = AB + AC