If left[ {begin{array}{*{20}{c}}{x + y}&{2x + z}{x - y}&{2z + w}end{array}} right] = left[ {

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3 and 4 .Determinants and Matrices

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If $\left[ {\begin{array}{{20}{c}}{x + y}&{2x + z}\\{x - y}&{2z + w}\end{array}} \right] = \left[ {\begin{array}{{20}{c}}4&7\\0&{10}\end{array}} \right]$, then values of $x, y, z, w$ are

A

$2, 2, 3, 4$

B

$2, 3, 1, 2$

C

$3, 3, 0, 1$

D

None of these

Solution

(a) Given, $x + y = 4$…..$(i)$

and $x – y = 0$ .…$(ii)$

After solving $(i)$ and $(ii),$ $x = 2,\,y = 2$

$\therefore$ $2x + z = 7$ $⇒$ $z = 3$ and $2z + w = 10$ $⇒$ $w = 4$.

Standard 12

Mathematics

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