Q18E Compute the products聽Ax鈫� 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: Q18E (page 35)

Compute the products $A \overset{鈫�}{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
18. $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$

Short Answer

Expert verified

The product of $A \overset{鈫�}{x}$ is, $[\begin{matrix} 5 \\ 11 \\ 17 \end{matrix}]$ .

Step by step solution

Consider the given matrices

If $A$ is an $n 脳 m$ 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,

$[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$

Here $A$ is $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}]$ and $\overset{鈫�}{x}$ is $[\begin{matrix} 1 \\ 2 \end{matrix}]$ .

Perform the operation

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

$\begin{matrix} [\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}] = [\begin{matrix} 1 鈰� 1 + 2 鈰� 2 \\ 3 鈰� 1 + 4 鈰� 2 \\ 5 鈰� 1 + 6 鈰� 2 \end{matrix}] \\ = [\begin{matrix} 5 \\ 11 \\ 17 \end{matrix}] \end{matrix}$

Hence, the required product is $[\begin{matrix} 5 \\ 11 \\ 17 \end{matrix}]$ .

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91影视

Compute the products $A \overset{鈫�}{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).
18. $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$

Short Answer

Step by step solution

Consider the given matrices

Perform the operation

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91影视

Compute the productsAx鈫� in Exercises 16 through 19 using paper and pencil (if the products are defined).18. [123456][12]

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

Mechanics Maths

Probability and Statistics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

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).
18. $[\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}]$