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Determine which of the matrices in Exercises $7-12$ are orthogonal. If orthogonal, find the inverse. $$\left[\begin{array}{ccc}{1 / 3} & {2 / 3} & {2 / 3} \\ {2 / 3} & {1 / 3} & {-2 / 3} \\ {2 / 3} & {-2 / 3} & {1 / 3}\end{array}\right]$$

Yes, the matrix is orthogonal

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 1

Diagonalization of Symmetric Matrices

Introduction to Matrices

Oregon State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

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it's given that dramatic C equals two. One by three Toe by three by three two by 31 My three minus two by 22 by three Minus two by 31 by three No a transpose Sequins one by three two by three Kobe three then two by three one by three minus to wait three and the hard colonies two by three minus two by three, one by a tree. If you want to play with magic c eight mitt transpose you will Yet one gentle, gentle Gino one Judo geul Geul Want the cheese equal to Okay, so we can say that the Grand Matics is Hey, our doe Gordon Magics. And we know that in tow inwards equals two. Right, So here a transfer was equals two The n word inverse matrix I So the investments metrics Amos equals two on my 32 by three to wait three to bay three one by three minus two by three To weigh three minus two by 31 break. Thank you for watching

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