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Question
Construct the matrix A = [aij]3×3, where aij = 1 – j. State whether A is symmetric or skew–symmetric
Solution
A = [aij]3×3
Where aij = 1 – j
A = `[("a"_11, "a"_12, "a"_13),("a"_21, "a"_22, "a"_23),("a"_31, "a"_32, "a"_33)]`
aij = i – j
a11 = 1 – 1 = 1
a12 = 1 – 2 = – 1
a13 = 1 – 3 = – 2
a21 = 2 – 1 = 1
a22 = 2 – 2 = 1
a23 = 2 – 3 = – 1
a31 = 3 – 1 = 2
a32 = 3 – 2 = 1
a33 = 3 – 3 = 0
A = `[(0, -1, -2),(1, 0, -1),(2, 1, 0)]`
AT = `[(0, 1, 2),(-1, 0, 1),(-2, -1, 0)]`
AT = `- [(0, -1, -2),(1, 0, -1),(2, 1, 0)]`
AT = – A
∴ A is skew-symmetric.
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