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

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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