JAC asked in Science & MathematicsMathematics · 1 decade ago

Find Orthogonal matrix (linear algebra)?

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

3 Answers

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  • 1 decade ago
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    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

  • 1 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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