Question

solve the matrix.......... ​

Answer 1

Answer:

x = 0

y = 27 / 2

y = 27 / 2

p = 9

Step-by-step explanation:

It is given that the value of $2\left[\begin{array}{cc}x&y\\z&p\end{array}\right] - 9\left[\begin{array}{cc}-2&3\\1&0\end{array}\right]\:is\:18\text {I}$

And, from the properties of matrix we know I = $\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

Therefore,

$\implies2\left[\begin{array}{cc}x&y\\z&p\end{array}\right] - 9\left[\begin{array}{cc}-2&3\\1&0\end{array}\right]\:is\:18\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

$\implies \left[\begin{array}{cc}2x&2y\\2z&2p\end{array}\right] - \left[\begin{array}{cc}-18&27\\9&0\end{array}\right]\:=\:\left[\begin{array}{cc}18&0\\0&18\end{array}\right]$

$\implies \left[\begin{array}{cc}2x-(-18)&2y-27\\2z-9&2p-0\end{array}\right] = \left[\begin{array}{cc}18&0\\0&18\end{array}\right]$

$\implies \left[\begin{array}{cc}2x+18&2y-27\\2z-9&2p-0\end{array}\right] = \left[\begin{array}{cc}18&0\\0&18\end{array}\right]$

Comparing values : -

= > 2x + 18 = 18

= > 2x = 0

= > x = 0

= > 2y - 27 = 0

= > 2y = 27

= > y = 27 / 2

= > 2z - 9 = 0

= > 2z = 9

= > y = 27 / 2

= > 2p = 18

= > p = 18 / 2

= > p = 9

Answer 2

$\underline{ \boxed{{ \huge{ \mathtt{M}}} \mathtt{ATRIX \: \: }}}$

Choose the correct alternative :

$\sf if \: 2 \left[ \begin{array}{c c } \sf x & \sf y \\ \\ \sf z& \sf \: p \end{array} \right] - 9 \left[ \begin{array}{c c } \sf - 2& \sf 3 \\\\ \sf \: 1& \sf \: 0 \end{array} \right] \: = 18 \mathtt{I}$

(a) X = 8 ; z = 9/2 (✔️)

(b) X = 0 ; z = -9/2

(c) X = 0 ; z = 9/2

(d) None of these

$\underline{ \underline{{ \mathtt{ \: \: \: ANSWER - }}}}$

$\implies{ \mathtt{\left[ \begin{array}{c c } \sf 2x& \sf 2y \\\\ \sf \: 2z& \sf \: 2p \end{array} \right] - \left[ \begin{array}{c c } \sf - 18& \sf 27 \\\\ \sf \: 9& \sf \: 0 \end{array} \right] = 18 \mathtt{I}}} \\ \\ \\ \implies{ \mathtt{\left[ \begin{array}{c c } \sf 2x - ( - 18)& \: \: \: \sf 2y - 27 \\\\ \sf \: 2z - 9& \sf \: 2p - 0 \end{array} \right] = 18\left[ \begin{array}{c c } \sf 1& \sf 0 \\\\ \sf \: 0& \sf \: 1 \end{array} \right]}} \\ \\ \\ \implies{ \mathtt{\left[ \begin{array}{c c } \sf 2x + 18& \: \: \: \sf 2y - 27\\\\ \sf \: 2z - 9& \: \: \: \sf \: 2p - 0 \end{array} \right] =\left[ \begin{array}{c c } \sf 18& \sf 0 \\\\ \sf \: 0& \sf \: 18 \end{array} \right] }} \\ \\ \\ \implies{ \mathtt{2x + 18 = 18}} \\ \implies{ \mathtt{2x = 18 - 18}} \\ \implies{ \mathtt{x = \frac{0}{2} }} \\ \boxed{ \purple{\therefore{ \mathtt{x = 0}}}} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \implies{ \mathtt{2z - 9 = 0 }} \\ \implies{ \mathtt{2z = 9}} \\ \implies{ \mathtt{z = \frac{9}{2} }} \\ \boxed{ \mathtt{ \purple{ \therefore{z = \frac{9}{2} }}}} \: \: \: \: \: \: \: \:$

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