Q42E In Exercise 40 through 46, consi... [FREE SOLUTION]

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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 5: Q42E (page 217)

In Exercise 40 through 46, consider vectors ${\overset{鈫�}{v}}_{1}, {\overset{鈫�}{v}}_{2}, {\overset{鈫�}{v}}_{3}$ in role="math" localid="1659606624550" $R^{4}$ ; we are told that ${\overset{鈫�}{v}}_{i}, {\overset{鈫�}{v}}_{j}$ is the entry data-custom-editor="chemistry" $a_{i j}$ of matrix A.
$A = [\begin{matrix} 3 & 5 & 11 \\ 5 & 9 & 20 \\ 11 & 20 & 49 \end{matrix}]$
Find $| | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | |$

Short Answer

Expert verified

The value of $| | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | |$ is $鈮� 4.69$ .

Step by step solution

Step by step answerStep 1: Given

The given matrix is $A = [\begin{matrix} 3 & 5 & 11 \\ 5 & 9 & 20 \\ 11 & 20 & 49 \end{matrix}]$ .

Determine the value of ||v→1+v→2||

To find the value of $| | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | |$ . Let us write the matrix in the ${\overset{鈫�}{v}}_{i} . {\overset{鈫�}{v}}_{j}$ notation.

Consider the terms below:

$A = [\begin{matrix} 3 & 5 & 11 \\ 5 & 9 & 20 \\ 11 & 20 & 49 \end{matrix}] = [\begin{matrix} {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{1} & {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{2} & {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{1} & {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{2} & {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{3} . {\overset{鈫�}{v}}_{1} & {\overset{鈫�}{v}}_{3} . {\overset{鈫�}{v}}_{2} & {\overset{鈫�}{v}}_{3} . {\overset{鈫�}{v}}_{3} \end{matrix}] = [\begin{matrix} | | {\overset{鈫�}{v}}_{1} | |^{2} & {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{2} & {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{1} & | | {\overset{鈫�}{v}}_{2} | |^{2} & {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{3} \\ {\overset{鈫�}{v}}_{3} . {\overset{鈫�}{v}}_{1} & {\overset{鈫�}{v}}_{3} . {\overset{鈫�}{v}}_{2} & | | {\overset{鈫�}{v}}_{3} | |^{2} \end{matrix}]$

Now, compute the above terms in the form of $| | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | |$ :

$| | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | |^{2} = ({\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2}) 路 ({\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2}) = {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{1} . {\overset{鈫�}{v}}_{2} + {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} . {\overset{鈫�}{v}}_{2} = 3 + 5 + 5 + 9 = 22 | | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | | = \sqrt{22} 鈮� 4.69$

Thus,

$| | {\overset{鈫�}{v}}_{1} + {\overset{鈫�}{v}}_{2} | | 鈮� 4.69$

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91影视

Short Answer

Step by step solution

Step by step answerStep 1: Given

Determine the value of ||v→1+v→2||

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91影视

In Exercise 40 through 46, consider vectors v鈫�1,v鈫�2,v鈫�3in role="math" localid="1659606624550" R4; we are told that v鈫�i,v鈫�jis the entry data-custom-editor="chemistry" aijof matrix A.A=[35115920112049]Find ||v鈫�1+v鈫�2||

Short Answer

Step by step solution

Step by step answerStep 1: Given

Determine the value of ||v→1+v→2||

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Mechanics Maths

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