Get Answers to all your Questions

header-bg qa

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

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support