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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 20 Maths Textbook Solution.

Answers (1)

Answer: x= 3,y= 1

Given:  \begin{bmatrix} x+10 & y^{2}+2y\\ 0& -4 \end{bmatrix}= \begin{bmatrix} 3x+4 & 3\\ 0& y^{2}-5y \end{bmatrix}

We have to find out the value of x  and y
Hint: We will use equality of matrices.

Solution:   Here \begin{bmatrix} x+10 & y^{2}+2y\\ 0& -4 \end{bmatrix}= \begin{bmatrix} 3x+4 & 3\\ 0& y^{2}-5y \end{bmatrix}

Since, corresponding entries of equal matrices are equal. So,

 x+10=3x+4                                                                                                                                ….. (i)

 y^{2}+2y= 3                                                                                                                                      ….. (ii)

-4= y^{2}-5y                                                                                                                                    ….. (iii)

Solving equation (i), We get

x+10= 3x+4\\\Rightarrow 2x=6\\\Rightarrow x=3

Solving equation (ii), We get

y^{2}+2y-3=0\\\Rightarrow y+3y-y-3=0\\\Rightarrow y\left ( y+3 \right )-1\left ( y+3 \right )=0\\\Rightarrow y=1\: or\: -3

Solving equation (iii), We get

-4=y^{2}-5y\\\Rightarrow y^{2}-5y+4=0\\\Rightarrow y^{2}-4y-y+4=0\\\Rightarrow y\left ( y-1 \right )-1( \left ( y-4 \right ) =0\\\Rightarrow \left ( y-1 \right )\left ( y-4 \right )=0\\\Rightarrow y=1\: or\: 4

From equation (ii) and (iii)
We have common value of y= 1
So, x= 3,y= 1

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