If the matrix is a symmetric matrix, find the values of x, y, z and t.

Engineering

Mathematics

Introduction to Matrix

Special Type of Square Matrices

Question

If the matrix $A = [\begin{array}{ccc} 5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7 \end{array}]$ is a symmetric matrix, find the values of x, y, z and t.

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$A = [\begin{array}{ccc} 5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7 \end{array}]$

\Rightarrow A^{T} = [\begin{array}{ccc} 5 & y & 4 \\ 2 & z & t \\ x & - 3 & - 7 \end{array}]

Since, A is symmetric matrix. So, (A^T) = A

\Rightarrow [\begin{array}{ccc} 5 & y & 4 \\ 2 & z & t \\ x & - 3 & - 7 \end{array}] = [\begin{array}{ccc} 5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7 \end{array}]

The corresponding elements of two equal matrices are equal.

So we get,

⇒ x = 4

⇒ y = 2

⇒ z = z

⇒ t = – 3