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Chapter 2: Q25E (page 108)

TRUE OR FALSE?

The matrix(111-1) represents a reflection about a line.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Reflection of a matrix

The reflection of the matrix is of the form (abb-a) where a2+b2=1. .

02

Compute the reflection of the matrix

Consider the matrix.

111-1

Here, a=b=1.

Consider the condition.

a2+b2=1鈬�12+12=2鈮�1

Therefore, the matrix reflection about a line does not exist.

Hence, the given statement is true.

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