Q49E Consider the vectorsu鈫�,v鈫抋nd... [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: Q49E (page 161)

Consider the vectors $\overset{鈫�}{u}, \overset{鈫�}{v}$ and $\overset{鈫�}{w}$ sketched in the accompanying figure. Find the coordinate vector of $\overset{鈫�}{w}$ with respect to the basis $\overset{鈫�}{u}, \overset{鈫�}{v}$ .

Short Answer

Expert verified

The coordinate vector of $\overset{鈫�}{w}$ with respect to the basis $\overset{鈫�}{u}, \overset{鈫�}{v}$ is-

${[\overset{鈫�}{w}]}_{貜} = [\begin{matrix} - 1 \\ - 1 \end{matrix}],$ where $貜 = \{\overset{鈫�}{u}, \overset{鈫�}{v}\}$

Step by step solution

Finding the vector w→

Let $貜 = \{\overset{鈫�}{u}, \overset{鈫�}{v}\}$ be the basis.

We know that the if resultant of two vector $\overset{鈫�}{u}, \overset{鈫�}{v}$ is $\overset{鈫�}{w}$ .

Then $\overset{鈫�}{w} = \overset{鈫�}{u} + \overset{鈫�}{v}$

But from the figure we can see that the vector $\overset{鈫�}{w}$ is in the opposite direction of $\overset{鈫�}{u} and \overset{鈫�}{v}$ , therefore we have

$- \overset{鈫�}{w} = \overset{鈫�}{u} + \overset{鈫�}{v} 鈬� \overset{鈫�}{w} = - \overset{鈫�}{u} - \overset{鈫�}{v} 鈬� \overset{鈫�}{w} = (- 1) \overset{鈫�}{u} + (- 1) \overset{鈫�}{v}$

Finding the coordinate vector of w→

Since we have

$\overset{鈫�}{w} = - \overset{鈫�}{u} + - \overset{鈫�}{v} 鈬� \overset{鈫�}{w} = (- 1) \overset{鈫�}{u} + (- 1) \overset{鈫�}{v} 鈬� {[\overset{鈫�}{w}]}_{貜} = [\begin{matrix} - 1 \\ - 1 \end{matrix}]$

Thus, the coordinate vector of $\overset{鈫�}{w}$ isrole="math" localid="1660379390895" ${[\overset{鈫�}{w}]}_{貜} = [\begin{matrix} - 1 \\ - 1 \end{matrix}] Where 貜 = \{\overset{鈫�}{u}, \overset{鈫�}{v}\}$ .

Final Answer

If $貜 = \{\overset{鈫�}{u}, \overset{鈫�}{v}\}$ be the basis and the vector $\overset{鈫�}{w}$ is resultant of the two vector $\overset{鈫�}{u,} \overset{鈫�}{v}$ then the coordinate vector of $\overset{鈫�}{w}$ is given by-

${[\overset{鈫�}{w}]}_{貜} = [\begin{matrix} - 1 \\ - 1 \end{matrix}] Where 貜 = \{\overset{鈫�}{u}, \overset{鈫�}{v}\}$

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91影视

Consider the vectors $\overset{鈫�}{u}, \overset{鈫�}{v}$ and $\overset{鈫�}{w}$ sketched in the accompanying figure. Find the coordinate vector of $\overset{鈫�}{w}$ with respect to the basis $\overset{鈫�}{u}, \overset{鈫�}{v}$ .

Short Answer

Step by step solution

Finding the vector w→

Finding the coordinate vector of w→

Final Answer

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91影视

Consider the vectorsu鈫�,v鈫�andw鈫�sketched in the accompanying figure. Find the coordinate vector of w鈫�with respect to the basisu鈫�,v鈫�.

Short Answer

Step by step solution

Finding the vector w→

Finding the coordinate vector of w→

Final Answer

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Applied Mathematics

Calculus

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Consider the vectors $\overset{鈫�}{u}, \overset{鈫�}{v}$ and $\overset{鈫�}{w}$ sketched in the accompanying figure. Find the coordinate vector of $\overset{鈫�}{w}$ with respect to the basis $\overset{鈫�}{u}, \overset{鈫�}{v}$ .