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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 15 Subquestion (i) Maths Textbook Solution.

Answers (1)

Answer: x = \frac{3}{2}\: and\: y = \frac{-3}{2}

Hint: Solve LHS and then equate with RHS.

Given:\begin{bmatrix} x-y &2 & -2\\ 4 &x & 6 \end{bmatrix} +\begin{bmatrix} 3 & -2 &2 \\ 1 & 0 &- 1 \end{bmatrix} = \begin{bmatrix} 6 & 0 & 0\\ 5 & 2x+y & 5 \end{bmatrix}

Here, we have to compute x  and y.

Solution:

  \begin{bmatrix} x-y &2 & -2\\ 4 &x & 6 \end{bmatrix} +\begin{bmatrix} 3 & -2 &2 \\ 1 & 0 &- 1 \end{bmatrix} = \begin{bmatrix} 6 & 0 & 0\\ 5 & 2x+y & 5 \end{bmatrix}

\begin{bmatrix} x-y+3 &2-2 & -2+2\\ 4+1 &x+0 & 6-1 \end{bmatrix} = \begin{bmatrix} 6 & 0 & 0\\ 5 & 2x+y & 5 \end{bmatrix}

Equating this, we get:

x-y + 3 = 6
\Rightarrow x-y = 3                                                                                                       … (1)

Also,

x = 2x + y
\Rightarrow y = -x                                                                                                …. (2)

Applying the value of ‘y’ in equation (1), we get:

x-(-x) = 3
2x = 3
x = \frac{3}{2}

Applying the value of ‘x ’ in equation (2), we get:

y = \frac{-3}{2}

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