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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 11 Maths Textbook Solution.

Answers (1)

Answer: $x=11,y=9,z=3$

Given: $A=B$

$\begin{bmatrix} x-2 & 3 &2z \\ 18z &y+2 & 6z \end{bmatrix}$ $= \begin{bmatrix} y & z &6\\ 6y&x & 2y \end{bmatrix}$

Hint: If $A=B\Rightarrow$ If two matrices are equal then the elements of each matrix are also equal.

Solution: Here $A=B$

$\begin{bmatrix} x-2 & 3 &2z \\ 18z &y+2 & 6z \end{bmatrix}$ $= \begin{bmatrix} y & z &6\\ 6y&x & 2y \end{bmatrix}$

Since corresponding entries of equal matrices are equal, So

$x-2=y$ ….. (i)

$3=z$ ….. (ii)

$2z=6$ ….. (iii)

$18z=6y$ ….. (iv)

$y+2=x$ ….. (v)

$6z=2y$ ….. (vi)

Equation (ii) gives $z=3$

Putting the value of z in eqn(iv) we get

$18\times 3=6y\\\Rightarrow y=9$

Putting the value of $y$ in eqn(v) we get

$y+2=x\\\Rightarrow 9+2=x\\\Rightarrow x=11$

Hence $x=11,y=9,z=3$

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