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If A = [01+2ii-2-1-2i0-72-i70] where i = -1 Prove that AT = – A - Mathematics and Statistics

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Question

If A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]` where i = `sqrt(-1)` Prove that AT = – A

Sum
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Solution

A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]` 

∴ AT = `[(0, -1 - 2"i", 2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)] ...(1)`

and – A = `-[(0,1 + 2"i","i" - 2),(-1 - 2"i", 0, -7),(2 - "i",7, 0)]`

= `[(0,-1 - 2"i",2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)] ...(2)`

From (1) and (2),

∴ AT = – A.

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Chapter 4: Determinants and Matrices - Exercise 4.7 [Page 97]

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