Question

Find out whether the matrix is Symmetric or not. ​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Let A=$\sf{\left[\begin{array}{c c c} 2&3&4\\ 3& 4&7\\4&7&8 \end{array}\right]}$

To find whether the matrix is symmetric or not we need to prove A'=A if it satisfies then the given matrix is symmetric.

A'=Means transpose

Transpose means exchange the rows and columns.

A'=$\sf{\left[\begin{array}{c c c} 2&3&4\\ 3& 4&7\\4&7&8 \end{array}\right]}$

Here,A'=A

Hence ,it satisfies the condition.

$\therefore$A=$\sf{\left[\begin{array}{c c c} 2&3&4\\ 3& 4&7\\4&7&8 \end{array}\right]}$is symmetric matrix.

Concept of transpose(A')

Let A=$\sf{\left[\begin{array}{c c c} 1&2&3\\ 4& 5&6\\7&8&9\end{array}\right]}$

Transpose (Exchanging rows and columns)

A'=$\sf{\left[\begin{array}{c c c} 1&4&7\\ 2& 5&8\\3&6&9 \end{array}\right]}$

Here,A' not equal to A so ,it is not a symmetric matrix.

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Let A=$\sf{\left[\begin{array}{c c c} 2&3&4\\ 3& 4&7\\4&7&8 \end{array}\right]}$

To find whether the matrix is symmetric or not we need to prove A'=A if it satisfies then the given matrix is symmetric.

A'=Means transpose

Transpose means exchange the rows and columns.

A'=$\sf{\left[\begin{array}{c c c} 2&3&4\\ 3& 4&7\\4&7&8 \end{array}\right]}$

Here,A'=A

Hence ,it satisfies the condition.

$\therefore$A=$\sf{\left[\begin{array}{c c c} 2&3&4\\ 3& 4&7\\4&7&8 \end{array}\right]}$is symmetric matrix.

Concept of transpose(A')

Let A=$\sf{\left[\begin{array}{c c c} 1&2&3\\ 4& 5&6\\7&8&9\end{array}\right]}$

Transpose (Exchanging rows and columns)

A'=$\sf{\left[\begin{array}{c c c} 1&4&7\\ 2& 5&8\\3&6&9 \end{array}\right]}$

Here,A' not equal to A so ,it is not a symmetric matrix.