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Chapter 6: Q18E (page 309)

The determinant of all orthogonal matrices is 1 .

Short Answer

Expert verified

Therefore, the given statement is false.

Step by step solution

01

Orthogonal Matrix Definition. 

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

02

To check whether the given condition is true or false. 

The determinant of the orthogonal matrix is equal to -1 or -1.

Since,

detA=detAT

and the determinant of product is the product of determinants. A when is an orthogonal matrix.

Therefore, the given statement is false.

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Most popular questions from this chapter

Find the determinants of the linear transformations in Exercises 17 through 28.

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An8脳8matrix fails to be invertible if (and only if) its determinant is nonzero.

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Consider two positive numbers a and b. Solve the following system:

|ax-by=1bx+ay=0|.

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Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

4.[1-12-2-1216211410-261033]
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