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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 15 Maths Textbook Solution.

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Answer: x+y=7  or -3

Given:  Given that

            \begin{bmatrix} 2x+1 &5x \\ 0 &y^{2}+1 \end{bmatrix}= \begin{bmatrix} x+3 &10\\ 0 & 26 \end{bmatrix}

Here we have to calculate the value of x+y

Hint:  Here we will use equality of matrices.

Solution: Here \begin{bmatrix} 2x+1 &5x \\ 0 &y^{2}+1 \end{bmatrix}= \begin{bmatrix} x+3 &10\\ 0 & 26 \end{bmatrix}

The corresponding entries of equal matrices are equal, So

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

 y^{2}+1=26\\\Rightarrow y^{2}=26-1\\\Rightarrow y=\sqrt{25}\\\Rightarrow y=\pm 5

Case 1: If x=2 and y=+5

\Rightarrow x+y=2+5=7

Case 2: If  x=2  and y=-5

\Rightarrow x+y=2+\left ( -5 \right )=-3

Hence x+y=7  or -3

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