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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 19 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 19 Maths Textbook Solution.

Answers (1)

Answer: A and B are not equal for any value of y

Given: A=\begin{bmatrix} 2x+1 &2y \\ 0 & y^{2}+2 \end{bmatrix}  and

            B=\begin{bmatrix} x+3 &y^{2}+2 \\ 0 & -6 \end{bmatrix}

We have to find out the value of x  and y
Hint: We will use equality of matrices.
Solution:   Here A=B
Since equal matrix have all corresponding entries equal. So,

2x+1=x+3                                                                                                                                           ….. (i)

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

y2-5y=-6                                                                                                                                           ….. (iii)

Solving equation (i), We get

2x+1=x+3\\\Rightarrow 2x-x=3-1\\\Rightarrow x=2

Solving equation (ii), We get

2y=y^{2}+2\\\Rightarrow y^{2}-2y+2=0\\\Rightarrow D=b^{2}-4ac

\! \! \! \! \! \! \! \! \! =\left ( -2 \right )^{2}-4\left ( 1 \right )\left ( 2 \right )\\=4-8\\=-4

Here D< 0
So, there is no real value of y  from equation (ii)
Solving equation (iii), We get

y^{2}5y=-6\\\Rightarrow y^{2}-5y+6=0\\\left ( y-3 \right )\left ( y-2 \right )=0\\y=3\: or\: 2

From solution of equation (i) (ii) and (iii)
we can say that A and B cannot equal for any value of  y

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