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  • Need solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 3

Need solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 3

Answers (1)

Answer:

 x = 2  and y = 1 so, 2x + y = 2(2) + 1 = 5

Hint:

 Use the basic concept of symmetric matrix.

Given:

 \text { Symmetric matrix } A=\left[\begin{array}{ccc} -1 & 2 & 3 x \\ 2 y & 4 & -1 \\ 6 & 5 & 0 \end{array}\right]

Solution:

A=AT

\begin{aligned} &\text { Here, } A=\left[\begin{array}{ccc} -1 & 2 & 3 x \\ 2 y & 4 & -1 \\ 6 & 5 & 0 \end{array}\right] \text { and } A^{T}=\left[\begin{array}{ccc} -1 & 2 y & 6 \\ 2 & 4 & 5 \\ 3 x & -1 & 0 \end{array}\right] \\ &{\left[\begin{array}{ccc} -1 & 2 & 3 x \\ 2 y & 4 & -1 \\ 6 & 5 & 0 \end{array}\right]=\left[\begin{array}{ccc} -1 & 2 y & 6 \\ 2 & 4 & 5 \\ 3 x & -1 & 0 \end{array}\right]} \end{aligned}

By comparing respective elements,

\begin{aligned} &\therefore 2 y=2 y=1 \\ &\text { And } 3 x=6 x=2 \\ &2 x+y=2(2)+1=5 \end{aligned}

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Gurleen Kaur

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