Q59E If A,B,C and D are noninvertible... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 4: Q59E (page 201)

If A,B,C and D are noninvertible $2 脳 2$ matrices then the matrices AB,BC, and AD must be linearly dependent.

Short Answer

Expert verified

Therefore, the givens statement is True.

Step by step solution

Determine the concept for non-invertible matrix as:

Consider the transformation as follows.

Consider the non-invertible matrices as follows.

$A = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}]] B = [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}], c = [\begin{matrix} 0 & 0 \\ 1 & 0 \end{matrix}] D = [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$

Explanation of the solution

Now, find AB, AC and AD as follows.

$A B = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] A C = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 0 \\ 1 & 0 \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

Simplify further as follows.

$A D = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

The above matrices are linearly dependent.

Thus, the given statement 鈥淚f A,B,C and D are non-invertible $2 脳 2$ matrices, then the matrices AB,AC and AD must be linearly dependent鈥� is true.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

If A,B,C and D are noninvertible $2 脳 2$ matrices then the matrices AB,BC, and AD must be linearly dependent.

Short Answer

Step by step solution

Determine the concept for non-invertible matrix as:

Explanation of the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Discrete Mathematics

Calculus

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

If A,B,C and D are noninvertible2脳2 matrices then the matrices AB,BC, and AD must be linearly dependent.

Short Answer

Step by step solution

Determine the concept for non-invertible matrix as:

Explanation of the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Discrete Mathematics

Calculus

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

If A,B,C and D are noninvertible $2 脳 2$ matrices then the matrices AB,BC, and AD must be linearly dependent.