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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 19 Subquestion (i) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 19 Subquestion (i) Maths Textbook Solution.

Answers (1)

Answer: x = 2, y = 4, z = 1, t =3
Hint: Solve LHS part and equate with RHS part.

Given: 3 \begin{bmatrix} x &y \\ z&t \end{bmatrix} = \begin{bmatrix} x &6 \\ -1 &2t \end{bmatrix} + \begin{bmatrix} 4 &x+y \\ z+t & 2t+3 \end{bmatrix}
Here, we have to compute x, y, z and t.
Solution:

3 \begin{bmatrix} x &y \\ z&t \end{bmatrix} = \begin{bmatrix} x &6 \\ -1 &2t \end{bmatrix} + \begin{bmatrix} 4 &x+y \\ z+t & 2t+3 \end{bmatrix}

\begin{bmatrix} 3x &3y \\ 3z&3t \end{bmatrix} = \begin{bmatrix} x &6 \\ -1 &2t \end{bmatrix} + \begin{bmatrix} 4 &x+y \\ z+t & 2t+3 \end{bmatrix}

\begin{bmatrix} 3x &3y \\ 3z&3t \end{bmatrix} = \begin{bmatrix} x+4 &6+x+y \\ -1+z+t &2t+3 \end{bmatrix}

Equating this, we get:

\! \! \! \! \! \! \! \! 3 x = x + 4\\ 2x = 4 \\ \Rightarrow x = 2                                                                                                     

Also,

\! \! \! \! \! \! \! \! 3y = 6 + x + y \\ 2y = 6 + x

Putting the value of ‘x ’, we get:

\! \! \! \! \! \! \! \! 2y = 6 + 2\\ 2y = 8\\ \Rightarrow y = 4     
Also,                                                                                                     

\! \! \! \! \! \! \! 3t = 2t + 3\\ \Rightarrow t = 3   

Now,

\! \! \! \! \! \! \! \! \! 3z = -1 + z + t\\ 2z = - 1 + t                                                                                            

Putting the value of ‘t’, we get:

\! \! \! \! \! \! \! 2z = -1 + 3\\ 2z = 2\\ \Rightarrow z = 1  

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