Express -eginbmatrix 18511-1 - 2lend bmatrix as the sum of a symmetric and a skew symmetric matrix-

Let A=[ 1 amp; 5; 1 amp; 2 ] A^1=[ 1 amp; 1; 5 amp; 2 ] Let P=A+A^1/2=1/2[ 2 amp; 4; 4 amp; 4 ]=[ 1 amp; 2; 2 amp; ...

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Standard XII

Mathematics

Skew Symmetric Matrix

Express 、egin...

Question

Express $[\begin{matrix} 1 & 5 - 1 & 2 \end{matrix}]$ as the sum of a symmetric and a skew symmetric matrix .

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Solution

$Let A = [\begin{matrix} 1 & 5 - 1 & 2 \end{matrix}] A^{1} = [\begin{matrix} 1 & - 1 5 & 2 \end{matrix}] Let P = \frac{A + A^{1}}{2} = \frac{1}{2} [\begin{matrix} 2 & 4 4 & 4 \end{matrix}] = [\begin{matrix} 1 & 2 2 & 2 \end{matrix}] Q = \frac{A - A^{1}}{2} = \frac{1}{2} [\begin{matrix} 0 & 6 - 6 & 0 \end{matrix}] = [\begin{matrix} 0 & 3 - 3 & 0 \end{matrix}]$

A = P + Q

Where P is symmetric and Q is skew symmetric

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Express $[\begin{matrix} 1 & 5 - 1 & 2 \end{matrix}]$ as the sum of a symmetric and a skew symmetric matrix .