Chapter 4: Q2. (page 171)

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
For any matrix $A_{m \times n}$ for $m \neq n$ , $A^{2}$ is defined.

Short Answer

Expert verified

The provided statement will never be true.

Step by step solution

Step 1- Consider any values of m and n

Consider m as 1 and n as 2.

– Write the matrices with dimensions

Split the matrix $A^{2}$

$A_{1 \times 2} \cdot A_{1 \times 2}$

As the inner dimensions are not the same which means that the matrix will not be defined.

Step 3- Write the conclusion

The provided statement will never be true due to same matrix and different count of row and columns.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
For any matrix $A_{m \times n}$ for $m \neq n$ , $A^{2}$ is defined.

Short Answer

Step by step solution

Step 1- Consider any values of m and n

– Write the matrices with dimensions

Step 3- Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Decision Maths

Mechanics Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.For any matrixAm×nform≠n , A2is defined.

Short Answer

Step by step solution

Step 1- Consider any values of m and n

– Write the matrices with dimensions

Step 3- Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Decision Maths

Mechanics Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
For any matrix $A_{m \times n}$ for $m \neq n$ , $A^{2}$ is defined.