Short Answer

If all the entries of a square matrix are 1 or 0, then must be 1, 0, or -1.

Therefore, the given condition is true.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: 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.

Step 2: To check whether the given condition is true or false.

For, $2 \times 2$ matrices whose entries are 0 and 1 , the determinant can only be -1, 0 , or 1.

For $n \times n$ matrices, where $n > 2$ , this applies using the Laplace expansion.

Therefore,

$d e t A = - 1, 0, 1$ .

Therefore, the given condition satisfied and the given statement is true.

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

If all the entries of a square matrix are 1 or 0, then must be 1, 0, or -1.

Step by Step Solution

Step 1: Orthogonal Matrix Definition.

Step 2: To check whether the given condition is true or false.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

If all the entries of a square matrix are 1 or 0, then must be 1, 0, or -1.

Step by Step Solution

Step 1: Orthogonal Matrix Definition.

Step 2: To check whether the given condition is true or false.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths