Question

please solved matrix ​

Answer 1

Question:-

Solve the following matrix equation for x and y

$: \implies \left[ \begin{array}{ccc} \rm \: x {}^{2} \\ \rm{y}^{2} \end{array} \right ] + 2\left[ \begin{array}{ccc} \rm \: 2x {}^{} \\ \rm{3y}^{} \end{array} \right ] = 3\left[ \begin{array}{ccc} \rm \: {7}^{} \\ \rm{ - 3}^{} \end{array} \right ]$

Solution:-

$\implies \left[ \begin{array}{ccc} \rm \: x {}^{2} \\ \rm{y}^{2} \end{array} \right ] + 2\left[ \begin{array}{ccc} \rm \: 2x {}^{} \\ \rm{3y}^{} \end{array} \right ] = 3\left[ \begin{array}{ccc} \rm \: {7}^{} \\ \rm{ - 3}^{} \end{array} \right ]$

$\implies \left[ \begin{array}{ccc} \rm \: x {}^{2} \\ \rm{y}^{2} \end{array} \right ] + \left[ \begin{array}{ccc} \rm \: 4x {}^{} \\ \rm{6y}^{} \end{array} \right ] = \left[ \begin{array}{ccc} \rm \: {21}^{} \\ \rm{ - 9}^{} \end{array} \right ]$

Now we have get

$\implies \rm {x}^{2} + 4x = 21$

$\rm \: \implies {y}^{2} + 6y = - 9$

Now take

$\implies \rm {x}^{2} + 4x = 21$

Using factorization method

$\implies \rm {x}^{2} + 4x - 21=0$

$\implies \rm {x}^{2} +7x - 3x - 21=0$

$\implies \rm x(x + 7) - 3(x + 7) = 0$

$\implies \rm (x - 3)(x + 7) = 0$

$\implies \rm x = 3 \: \: \: and \: \: x = - 7$

So value of x = 3 and x = - 7

Now take

$\rm \: \implies {y}^{2} + 6y = - 9$

$\implies \rm {y }^{2} + 6y+ 9 = 0$

$\implies \rm y {}^{2} + 3y + 3y + 9 = 0$

$\implies \rm y(y + 3) + 3(y + 3) = 0$

$\implies \rm (y + 3)(y + 3) = 0$

$\implies \rm y = - 3 \: \: \: and \: \: y = - 3$

So value of y = - 3 and y = - 3