Identify orthogonal matrices Invert orthogonal matrice begin{bmatrix}frac{1}{3} & frac{2}{3}&frac{2}{3} frac{2}{3} & frac{1}{3}&-frac{2}{3}frac{2}{3}&-frac{2}{3}&frac{1}{3} end{bmatrix}

Joni Kenny 2020-12-09 Answered
Identify orthogonal matrices Invert orthogonal matrice
[132323231323232313]
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berggansS
Answered 2020-12-10 Author has 91 answers
Step 1
To identify the orthogonal matrix
[132323231323232313]
Step 2
Note that a matrix is orthogonal if it satisfies:
AAT=I
A=[132323231323232313]AT=[132323231323232313]
AAT=[132323231323232313][132323231323232313]
=[19+49+4929+29492949+2929+294949+19+494929292949+2949292949+19+49]
=[100010001]=I
Step 3
Thus matrix is orthogonal.
Now note that the inverse of orthogonal matrix can be find as:
AAT=I
A1=AT
A1=[132323231323232313]
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Jeffrey Jordon
Answered 2022-01-27 Author has 2047 answers

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