Question

q 9. Find the value
of x and y (matrix) if
[1 1 / 4 5][x y] = [2 / 7]

Answer 1

Answer:

x=3, y= -1

HOPE IT HELPS YOU

Answer 2

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

$\: \: \: \: \: \: \: \: \: \: \: \: \bull \: \: \: \begin{bmatrix} 1 & 1\\ 4 & 5\end{bmatrix} \begin{bmatrix} \: x \\ y \end{bmatrix} = \begin{bmatrix} \: 2 \\ 7\end{bmatrix}$

$\large\underline{\sf{To\:Find - }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \bull \: \: \sf \: values \: of \: x \: and \: y$

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

↝ Given that

$\rm :\longmapsto\:\begin{bmatrix} 1 & 1\\ 4 & 5\end{bmatrix}\begin{bmatrix} \: x \\ y \end{bmatrix} = \begin{bmatrix} \: 2 \\ 7 \end{bmatrix}$

$\rm :\longmapsto\:\begin{bmatrix} \: x \times 1 + y \times 1 \\ 4 \times x + 5 \times y \end{bmatrix} = \begin{bmatrix} \: 2 \\ 7 \end{bmatrix}$

$\rm :\longmapsto\:\begin{bmatrix} \: x + y \\ 4x + 5y \end{bmatrix} = \begin{bmatrix} \: 2 \\ 7 \end{bmatrix}$

↝ On Comparing, we get

$\rm :\longmapsto\:x + y = 2 - - - (1)$

and

$\rm :\longmapsto\:4x + 5y = 7 - - - (2)$

↝ Multiply equation (1) by 5, we get

$\rm :\longmapsto\:5x + 5y = 10 - - - (3)$

↝ On Subtracting equation (2) from equation (3), we get

$\rm :\longmapsto\:5x + 5y - 4x - 5y = 10 - 7$

$\bf\implies \:x \: = \: 3 - - - (4)$

↝ On substituting 'x = 3', in equation (1), we get

$\rm :\longmapsto\:3 + y = 2$

$\bf\implies \:y \: = \: - \: 1$

$\overbrace{ \underline { \boxed { \rm \therefore \: The \: value \: of \: \: \: \boxed{ \bf \: x = 3} \: \: \: and \: \: \: \boxed{ \bf \: y = - 1} }}}$

Additional Information :-

Properties of Matrix Multiplication

• 1. Associative Property : A(BC) = (AB)C

• Distributive Property : A(B + C) = AB + AC

• Distributive Property : (A + B)C = AC + BC

• There exist Identity Matrix I such that AI = IA = A is called Multiplicative Identity.