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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 3 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 3 Maths.

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Answer: x = 4, y = 2, z\: \epsilon \: c, t = -3

Hint: If A is symmetric matrix, then A = A^{T}

Given: A = \begin{bmatrix} 5 &2 &x \\ y& z &-3 \\ 4& t &-7 \end{bmatrix}

Solution:

A^{T} = \begin{bmatrix} 5 &y &4 \\ 2& z &t \\ x& -3 &-7 \end{bmatrix}

We know that, A = A^{T}

\Rightarrow \begin{bmatrix} 5 &2 & x\\ y &z &-3 \\ 4& t &-7 \end{bmatrix}= \begin{bmatrix} 5 & y &4 \\ 2 &z & t\\ x& -3 &-7 \end{bmatrix}

Hence, we get

x = 4, y = 2, z = z, t = - 3

x = 4, y = 2, z\: \epsilon \: c, t = - 3

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