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#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 14 Maths Textbook Solution.

Answer:  $x=-3,y=-5,z=2,a=-2,b=-7,c=-1$

Given:   $\begin{bmatrix} x+3 &z+4 & 2y-7\\ 4x+6 &a-1 &0 \\ b-3& 3b &z+2c \end{bmatrix}$   $= \begin{bmatrix} 0 &6 &3y-2 \\ 2x & -3 &2c+2 \\ 2b+4 & -21 & 0 \end{bmatrix}$

Here we have to find out all the values of $x,y,z,a,b,c$

Hint: By definition of equal matrices is $A=\left [ a_{ij} \right ]_{m\times n}$  and  $B=\left [ b_{ij} \right ]_{m\times n}$  are equal then

$a_{ij}=b_{ij}$   for $i=1,2,3....m$  and  $j=1,2,3....n$

Solution: Given that $\begin{bmatrix} x+3 &z+4 & 2y-7\\ 4x+6 &a-1 &0 \\ b-3& 3b &z+2c \end{bmatrix}$  $= \begin{bmatrix} 0 &6 &3y-2 \\ 2x & -3 &2c+2 \\ 2b+4 & -21 & 0 \end{bmatrix}$

Equating the entries, we get

$x+3=0\\\Rightarrow x=-3$       ;       $z+4=6\\\Rightarrow z=2$          ;        $2y-7=3y-2\\\Rightarrow 2y-3y=-2+7\\\Rightarrow -y=+5\\\Rightarrow y=-5$

Similarly,

$a-1=-3$            and      $z+2c=0$

$\Rightarrow a=-3+1$      and       $2+2c=0$

$\Rightarrow a=-2$            and       $c=-1$

Lastly,

$b-3=2b+4\\\Rightarrow b-2b=4+3\\\Rightarrow -b=7\\\Rightarrow b=-7$

Hence, $x=-3,y=-5,z=2,a=-2,b=-7,c=-1$