જો 2left[begin{array}{ll}x & z y & tend{array}right]+3left[begin{array}{cc}1 & -1 0

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3 and 4 .Determinants and Matrices

easy

જો $2\left[\begin{array}{ll}x & z \\ y & t\end{array}\right]+3\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]=3\left[\begin{array}{ll}3 & 5 \\ 4 & 6\end{array}\right]$ હોય, તો $x,\, y, \,z$ અને $t$ માટે સમીકરણ ઉકેલો.

A

$x=3,\, y=6, \,z=9,$ $t=6$

B

$x=3,\, y=6, \,z=9,$ $t=6$

C

$x=3,\, y=6, \,z=9,$ $t=6$

D

$x=3,\, y=6, \,z=9,$ $t=6$

Solution

$2\left[\begin{array}{ll}x & z \\ y & t\end{array}\right]+3\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]=3\left[\begin{array}{ll}3 & 5 \\ 4 & 6\end{array}\right]$

$\Rightarrow\left[\begin{array}{ll}2 x & 2 z \\ 2 y & 2 t\end{array}\right]+\left[\begin{array}{cc}3 & -3 \\ 0 & 6\end{array}\right]=\left[\begin{array}{cc}9 & 15 \\ 12 & 18\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}2 x+3 & 2 z-3 \\ 2 y & 2 t+6\end{array}\right]=\left[\begin{array}{cc}9 & 15 \\ 12 & 18\end{array}\right]$

Comparing the corresponding elements of these two matrices, we get:

$2 x+3=9$

$\Rightarrow 2 x=6$

$\Rightarrow x=3$

$2 y=12$

$\Rightarrow y=6$

$2 z-3=15$

$\Rightarrow 2 z=18$

$\Rightarrow $ $=9$

$2 t+6=18$

$\Rightarrow 2 t=12$

$\Rightarrow t=6$

$\therefore $ $x=3,\, y=6, \,z=9,$ and $t=6$

Standard 12

Mathematics

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