Q19E Compute the productsAx鈫捖� in E... [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 1: Q19E (page 35)

Compute the products $A \overset{鈫�}{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
19. $[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$

Short Answer

Expert verified

The product $A \overset{鈫�}{x}$ of , $[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$ is. $[\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}]$

Step by step solution

Consider the given matrices

If $A$ is anrole="math" localid="1659684733594" $n 脳 m$ matrix with row vectors ${\overset{鈫�}{蝇}}_{1}, . ...., {\overset{鈫�}{蝇}}_{n}$ and $\overset{鈫�}{x}$ is a vector in ${鈩�}^{m}$ then,.

$A \overset{鈫�}{x} = [\begin{matrix} 鈭� {\overset{鈫�}{蝇}}_{1} 鈭� \\ 鈰� \\ 鈭� {\overset{鈫�}{蝇}}_{n} 鈭� \end{matrix}] \overset{鈫�}{x} = [\begin{matrix} 鈭� {\overset{鈫�}{蝇}}_{1} 鈰� \overset{鈫�}{x} 鈭� \\ 鈰� \\ 鈭� {\overset{鈫�}{蝇}}_{n} 鈰� \overset{鈫�}{x} 鈭� \end{matrix}]$

The given expression is,

$[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$

Here $A$ is $[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}]$ and $\overset{鈫�}{x}$ is $[\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$ .

Perform the operation

Now, find the product by performing the row column operations as follow:

$\begin{matrix} [\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}] = [\begin{matrix} 1 鈰� 1 + 1 鈰� 2 + (鈭� 1) 鈰� 3 \\ (鈭� 5) 鈰� 1 + 1 鈰� 2 + 1 鈰� 3 \\ 1 鈰� 1 + (鈭� 5) 鈰� 2 + 3 鈰� 3 \end{matrix}] \\ = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}] \end{matrix}$

Hence, the required product is

[\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}]

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

Compute the products $A \overset{鈫�}{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
19. $[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$

Short Answer

Step by step solution

Consider the given matrices

Perform the operation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Pure Maths

Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Compute the productsAx鈫� in Exercises 16 through 19 using paper and pencil (if the products are defined).19.[11鈭�1鈭�5111鈭�53][123]

Short Answer

Step by step solution

Consider the given matrices

Perform the operation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Pure Maths

Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Compute the products $A \overset{鈫�}{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
19. $[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$