Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q15E (page 308)

15.If the determinant of a $4 脳 4$ matrix $A$ is $4$ , then its rank must be $4$ .

Short Answer

Expert verified

Therefore, the given statement is false.

Step by step solution

Matrix Definition

Matrix is aset of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are $m$ rows and $n$ columns, the matrix is said to be a 鈥� $m$ by $n$ 鈥� matrix, written 鈥� $m 脳 n$ .鈥�

To check whether the given condition is true or false

For example, if

$A = [\begin{matrix} 2 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & \frac{1}{2} & 0 \\ 0 & 0 & 0 & 2 \end{matrix}]$

Then

$A = [\begin{matrix} 2 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & \frac{1}{2} & 0 \\ 0 & 0 & 0 & 2 \end{matrix}]$

det $d e t A = 2 [\begin{matrix} 2 & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & 2 \end{matrix}] d e t A = 2 (2 \frac{2}{2} - 0) d e t A = 4$

But $A = \frac{13}{2}$

Therefore, the given statement is false.

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

15.If the determinant of a $4 脳 4$ matrix $A$ is $4$ , then its rank must be $4$ .

Short Answer

Step by step solution

Matrix Definition

To check whether the given condition is true or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

91影视

15.If the determinant of a4脳4 matrix Ais 4, then its rank must be 4.

Short Answer

Step by step solution

Matrix Definition

To check whether the given condition is true or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

15.If the determinant of a $4 脳 4$ matrix $A$ is $4$ , then its rank must be $4$ .