Question

Solve the matrix equation.
​

Answer 1

Answer:

2x^2 -9x

12x. 0

is the answer

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:\: \begin{bmatrix} 2x & 3\end{bmatrix}\: \begin{bmatrix} 1 & 2\\ - 3 & 0\end{bmatrix}\: \begin{bmatrix} x\\ 3\end{bmatrix} = O$

$\rm :\longmapsto\:\: \begin{bmatrix} 2x - 9 & 4x + 0\end{bmatrix}\: \: \begin{bmatrix} x\\ 3\end{bmatrix} = O$

$\rm :\longmapsto\:\: \begin{bmatrix} 2x - 9 & 4x\end{bmatrix}\: \: \begin{bmatrix} x\\ 3\end{bmatrix} = O$

$\rm :\longmapsto\:\: \begin{bmatrix} x(2x - 9) + 4x \times 3\end{bmatrix}\: = \: \begin{bmatrix} 0\end{bmatrix}$

$\rm :\longmapsto\:\: \begin{bmatrix} 2 {x}^{2} - 9x + 12x \end{bmatrix}\: = \: \begin{bmatrix} 0\end{bmatrix}$

$\rm :\longmapsto\:\: \begin{bmatrix} 2 {x}^{2} + 3x \end{bmatrix}\: = \: \begin{bmatrix} 0\end{bmatrix}$

$\rm :\implies\: {2x}^{2} + 3x = 0$

$\rm :\longmapsto\:x(2x + 3) = 0$

$\bf\implies \:x = 0 \: \: \: or \: \: \: x = - \dfrac{3}{2}$

Additional Information :-

1. If A and B are two matrices, then AB is possible only when number of columns if matrix A is equals to number of rows of matrix B.

2. If A and B are two matrices, then matrix addition or subtraction is possible only when A and B are of same order.

3. Matrix multiplication may or may not be Commutative.

4. Matrix multiplication is Associative, i.e. A(BC) = (AB)C

5. Matrix multiplication is Distributive, i.e. A(B + C) = AB + AC.