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

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

Answers (1)

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

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