Practice set third

 Express the following matrices as sum of Symmetric and Skew-Symmetric matrices.

(1).  \(A=\left[\begin{array}{ccc}4 & 2 & -3 \\ 1 & 3 & -6 \\ -5 & 0 & -7\end{array}\right]\)

(2).  \(B=\left[\begin{array}{ccc}1 & 0 & 0 \\ -2 & 1 & 3 \\ 0 & 0 & 1\end{array}\right]\)

(3). \(C=\left[\begin{array}{ccc}0 & -1 & 1 \\ 1 & 0 & 4 \\ -1 & -4 & 0\end{array}\right]\)

(4). \(D=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 1 & 5 \\ 3 & 5 & 1\end{array}\right]\)

(5).  \(E=\left[\begin{array}{lll}1 & 2 & 8 \\ 6 & 4 & 5 \\ 1 & -1 & -2\end{array}\right]\)


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