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Chapter 6: Q40E (page 291)

IfA is an orthogonal matrix, what are the possible values ofdetA?

Short Answer

Expert verified

Therefore, the possible value of detAis given by, detA=卤1.

Step by step solution

01

Step by Step Solution:                  Step 1: Matrix Definition

Matrix is aset of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are mrows and ncolumns, the matrix is said to be a 鈥� mby n鈥� matrix, written 鈥� m脳n.鈥�

02

To find the possible value of  detA

If Ais an orthogonal matrix, then ATA=AAT=I, which leads us to:

1=det1=detAAT1=detAdetAT1=detAdetA1=(detA)2

So, detA=卤1

Therefore, the possible value of detAis given bydetA=卤1,

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