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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 8 Maths Textbook Solution.

Answers (1)

Answer:  a= 0,b=5,x=2  and  y= -1
Given: Here given that

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

We have to find the value of  a,b,x   and  y
Hint:  If two matrices are equal then the elements of each matrix are also equal.
Solution:  Given that two matrices are equal
\therefore  By equating them, we get
3x+4y                                                                                                                                       ……(i)
x-2y                                                                                                                                         ……(ii)
a+b= 5                                                                                                                                           ……. (iii)
2a-b= -5                                                                                                                                     …….. (iv)
Multiplying equation (ii) by 2 and adding to equation (i), we get
\! \! \! \! \! \! \! \! 3x+4y+2x-4y= 2+8\\\Rightarrow 5x= 10\\\Rightarrow x= 2
Now substituting the value of x in eqn (i), we get
3\times 2+4y= 2\\\Rightarrow 6 +4y= 2\\\Rightarrow 4y= -4\\\Rightarrow y= -1
Now by adding eqn(iii) and eqn (iv)
a+b+2a-b=5+\left ( -5 \right )
\Rightarrow 3a= 5-5
\Rightarrow a= 0

Now, again substituting the value of a  in eqn(iii), we get
a+b= 5
\Rightarrow b=5

Hence, a=0,b=5,x=2  and  y=-1

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