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# Find Orthogonal matrix (linear algebra)?

find an orthogonal matrix whose first row is (1/3, 2/3, 2/3 )?

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- ymail493Lv 51 decade agoFavorite Answer
first row: 1/3, 2/3, 2/3 (given)

second row: 2/3, 1/3, -2/3

third row: 2/3, -2/3, 1/3

- 7 years ago
Find an orthogonal matrix whose first row is (1/3, 2/3, 2/3).? complete solution

- modulo_functionLv 71 decade ago
What do you mean by 'orthogonal matrix'? Vectors or subspaces are orthogonal, I don't know about matrices.

OK, I looked it up. A matrix is orthogonal if it's transpose equals its inverse. This it must be square. So, you're looking for the 3x3 whose first row is given

You need a first column such that the dot product of your given row and the first column is 1 You also need the same diagonal so that

m11 = 1/3

This doesn't really seem like the best approach.

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