Question

( int )
(1) Let ( A=left[begin{array}{ccc}6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3end{array}right] ) (note: A isasymmetie
We know, symmetic math ( x=frac{1}{2}(A+A) )
[
begin{array}{l}
=frac{1}{2}left(left[begin{array}{ccc}
6 & -2 & 2
-2 & 3 & -1
2 & -1 & 3
end{array}right]+left[begin{array}{ccc}
6 & -2 & 2
-2 & 3 & -1
2 & -1 & 3
end{array}right]right)
= & frac{1}{2}left[begin{array}{ccc}
12 & -4 & 4
-4 & 6 & -2
4 & -2 & 6
end{array}right]
= & {left[begin{array}{ccc}
6 & -2 & 2
-2 & 3 & -1
2 & -1 & 3
end{array}right]}
end{array}
]
Skew symmeric matoix = ( frac{1}{2}left(A vec{F} A^{prime}right) )
[
=frac{1}{2}left{left[begin{array}{rrr}
6 & -2 & 2
-2 & 3 & -1
2 & -1 & 3
end{array}right]-left[begin{array}{rrr}
6 & -2 & 2
-2 & 3 & -1
2 & -1 & 3
end{array}right]right.
]
( =left[begin{array}{lll}0 & 0 & 0 0 & 0 & 0 0 & 0 & 0end{array}right] )

# T6 2 Express the matrix -2 3 12. – 27 -1 as the sum of a symmetric and a skew-symmetric matrix, 3

Solution