Q3.3-6E In Exercises 1聽through 20, , fi... [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 3: Q3.3-6E (page 143)

In Exercises 1through 20, , find the redundant column vectors of the given matrix $A$ 鈥渂y inspection.鈥� Then find a basis of the image of $A$ and a basis of the kernel of $A$ .
$(\begin{matrix} 1 & 1 & 3 \\ 2 & 1 & 4 \end{matrix})$

Short Answer

Expert verified

The relation between the vectors is, ${\overset{鈫�}{v}}_{1} + 2 {\overset{鈫�}{v}}_{2} - {\overset{鈫�}{v}}_{3} = 0$ . The basis of the image is, $[\begin{matrix} 1 \\ 2 \end{matrix}], [\begin{matrix} 1 \\ 1 \end{matrix}]$ and the basis of the kernel is, $[\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}]$ .

Step by step solution

Consider the matrix

The matrix is,

$(\begin{matrix} 1 & 1 & 3 \\ 2 & 1 & 4 \end{matrix})$

Check for the image and kernel of the matrix

The vectors are ${\overset{鈫�}{v}}_{1} = [\begin{matrix} 1 \\ 2 \end{matrix}], {\overset{鈫�}{v}}_{2} = [\begin{matrix} 1 \\ 1 \end{matrix}]$ , and ${\overset{鈫�}{v}}_{3} = [\begin{matrix} 3 \\ 4 \end{matrix}]$ .

Find the rref of the given matrix.

$r e f f (\begin{matrix} 1 & 1 & 3 \\ 2 & 1 & 4 \end{matrix}) = (\begin{matrix} 2 & 1 & 4 \\ 0 & \frac{1}{2} & 1 \end{matrix}) = (\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 2 \end{matrix})$

The relation can be defined as,

${\overset{鈫�}{v}}_{1} + 2 {\overset{鈫�}{v}}_{2} - {\overset{鈫�}{v}}_{3} = 0 [\begin{matrix} {\overset{鈫�}{v}}_{1} \\ {\overset{鈫�}{v}}_{2} \\ {\overset{鈫�}{v}}_{3} \end{matrix}] = [\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}]$

The image of the matrix is, $[\begin{matrix} 1 \\ 2 \end{matrix}], [\begin{matrix} 1 \\ 1 \end{matrix}]$ .

The kernel of the matrix is, localid="1664269579616" $[\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}]$ .

Final answer

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

In Exercises 1through 20, , find the redundant column vectors of the given matrix $A$ 鈥渂y inspection.鈥� Then find a basis of the image of $A$ and a basis of the kernel of $A$ .
$(\begin{matrix} 1 & 1 & 3 \\ 2 & 1 & 4 \end{matrix})$

Short Answer

Step by step solution

Consider the matrix

Check for the image and kernel of the matrix

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

91影视

In Exercises 1through 20, , find the redundant column vectors of the given matrix A鈥渂y inspection.鈥� Then find a basis of the image of A and a basis of the kernel of A.(113214)

Short Answer

Step by step solution

Consider the matrix

Check for the image and kernel of the matrix

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 1through 20, , find the redundant column vectors of the given matrix $A$ 鈥渂y inspection.鈥� Then find a basis of the image of $A$ and a basis of the kernel of $A$ .
$(\begin{matrix} 1 & 1 & 3 \\ 2 & 1 & 4 \end{matrix})$