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Use the accompanying figure to write each vector listed in Exercises 7 and 8 as a linear combination of $\mathbf{u}$ and $\mathbf{v} .$ Is every vector in $\mathbb{R}^{2}$ a linear combination of $\mathbf{u}$ and $\mathbf{v} ?$Vectors $\mathbf{a}, \mathbf{b}, \mathbf{c},$ and $\mathbf{d}$

Each vector is a linear comhination of $\mathbf { u } + \mathbf { v }$ since:$a = \mathbf { u } - 2 \mathbf { v }$$b = 2 \mathbf { u } - 2 \mathbf { v }$$c = 2 \mathbf { u } - 3.5 \mathbf { v }$$d = 3 \mathbf { u } - 4 \mathbf { v }$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

McMaster University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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02:26

Use the accompanying figur…

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In Exercises $1-8,$ use th…

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For each pair of vectors $…

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Write each vector as a lin…

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For the following exercise…

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In Exercises 21–38, let.

All right. So to do this problem, we want Teoh go to point a through D by moving with Well, the only the vectors v and you from the origin. This deals with the parallelogram rule for addition and is only possible because u and V are both linearly independent. So by this logic, what that means is a would equal a eagles You minus two V. So we're moving you vector up and to the left to V be with you. Cool. Two u minus to V. We move to you vector up and then to be to the left. See? Would you go to you minus 3.5 v And last but not least, d we're equal. Three U minus four v again, These are all just moving from the origin from 00 The origin to these points using only the vectors you envied moved to this to this location of point A, B, C and D

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In mathematics, the absolute value or modulus |x| of a real number x is its …

Use the accompanying figure to write each vector listed in Exercises 7 and 8…

In Exercises $1-8,$ use the given vectors to find $\mathbf{v} \cdot \mathbf{…

For each pair of vectors $\mathbf{u}$ and $\mathbf{v}$ given, compute (a) th…

Write each vector as a linear combination of the unit vectors i and $\mathbf…

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An important concern in the study of heat transfer is to determine the stead…

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In Exercises $25-28$ , determine if the specified linear transformation is (…

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$[\mathbf{M}]$ Let $\mathbf{b}=\left[\begin{array}{l}{7} \\ {5} \\ {9} \\ {7…

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In Exercises $19-22,$ convert the angle measure.(See Example. 5.)Con…

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PROBLEM SOLVING Over 2000 years ago, the Greek scholar Eratosthenes estimate…

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