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Chapter 5: Q1E (page 233)

Use the various characterizations of orthogonal transformations and orthogonal matrices. Find the matrix of an orthogonal projection. Use the properties of the transpose. Which of the matrices in Exercise 1 through 4 are orthogonal? [0.60.80.80.6].

Short Answer

Expert verified

The Matrix 0.60.80.80.6is not orthogonal.

Step by step solution

01

Definition of Orthogonal.

A square matrix is orthogonal matrix if A脳AT=I.

02

Verification whether the given matrix is orthogonal.

Let the given matrix isA=0.60.80.80.6 .

Then, the transpose of the given matrix isAT=0.60.80.80.6.

Thus,for orthogonal matrix,

A脳AT=0.60.80.80.6脳0.60.80.80.6=0.6脳0.6+0.8脳0.6+0.80.80.60.80.60.8+0.80.8+0.80.60.60.6=10.960.961

Since, the matrix not satisfy orthogonal conditionit givesA脳AT鈮�I. .

Hence,A=0.60.80.80.6 is not an orthogonal matrix.

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