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Chapter 5: Q21E (page 263)

The determinant of all orthogonal 2 脳 2 matrices is 1.

Short Answer

Expert verified

False

Step by step solution

01

Step by step solutionStep 1: Orthogonal matrix

Inlinear algebra, an orthogonal matrix, is a realsquare matrixwhose columns and rows areorthonormalvectors.

One way to express this isQTQ=QQT=IwhereQTis thetransposeofQandIis theidentity matrix.

02

Determine whether the statement is true or false

For example,

  • 1001 (identity transformation)
  • det-1001=1

Hence, the statement is false.

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Most popular questions from this chapter

Consider a line Lin Rn, spanned by a unit vector

u鈫�=[u1u2...un]

Consider the matrix Aof the orthogonal projection onto L. Describe the ijth entry of A, in terms of the componentsu鈫�iof u鈫�.

If then脳n matrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well?B-1.

TRUE OR FALSE?If matrix A is orthogonal, then the matrixAT must be orthogonal as well.

Question:TRUE OR FALSE?If matrices A and Bare commute, then A must commuteBT withas well.

Using paper and pencil, perform the Gram-Schmidt process on the sequences of vectors given in Exercises 1 through 14.

10.[1111],[6464]
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