# 10 True of False Problems about Nonsingular / Invertible Matrices

## Problem 500

10 questions about nonsingular matrices, invertible matrices, and linearly independent vectors.

The quiz is designed to test your understanding of the basic properties of these topics.

You can take the quiz as many times as you like.

The solutions will be given after completing all the 10 problems.
Click the View question button to see the solutions.

Notations: $I$ denotes an identity matrix and $O$ denotes a zero matrix.
The sizes of these matrices should be determined from the context.

## 10 True or False Problems about Nonsingular Matrix Operations

Determine whether each of the following sentences are True or False.

Notations: $I$ denotes an identity matrix and $O$ denotes a zero matrix. The sizes of these matrices should be determined from the context.

### 4 Responses

1. john kilbourne says:

“The row echelon form of an 3×3 matrix” – I don’t think this is always invertible.

If A =
110
110
110

The row echelon form of A is

110
000
000

If I am wrong on that, please let me know.

• Yu says:

Dear john kilbourne,

Thank you for your comment. You are right. In the problem, “invertible” was missing.

“The row echelon form of an 3×3 matrix” was a mistake. The correct problem should be:

“The row echelon form of an invertible 3×3 matrix”.

Thank you for pointing out this.

1. 07/04/2017

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2. 07/06/2017

[…] Or try True or False problems about nonsingular, invertible matrices, and linearly independent vectors at “10 True of False Problems about Nonsingular / Invertible Matrices“. […]

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