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  • Which of the following statements are True or False If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

Which of the following statements are True or False
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

Answers (1)

True

For example,

\begin{array}{l} \text { Let } A=\left[\begin{array}{lll} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 4 & 1 \end{array}\right], B=\left[\begin{array}{lll} 4 & 5 & 7 \\ 5 & 5 & 6 \\ 7 & 6 & 9 \end{array}\right] \end{array}  and C = \begin{bmatrix} 3 &9 &1 \\ 9 &2 &8 \\1 &8 &5 \end{bmatrix}

\Rightarrow A+B+C=\left[\begin{array}{lll} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 4 & 1 \end{array}\right]+\left[\begin{array}{lll} 4 & 5 & 7 \\ 5 & 5 & 6 \\ 7 & 6 & 9 \end{array}\right]+\left[\begin{array}{lll} 3 & 9 & 1 \\ 9 & 2 & 8 \\ 1 & 8 & 5 \end{array}\right]

A+B+C=\left[\begin{array}{lll} (1+4+3) & (2+5+9) & (3+7+1) \\ (2+5+9) & (1+5+2) & (4+6+8) \\ (3+7+1) & (4+6+8) & (1+9+5) \end{array}\right]

A+B+C=\left[\begin{array}{ccc} 8 & 16 & 11 \\ 16 & 8 & 18 \\ 11 & 18 & 15 \end{array}\right]

 

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