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Mark each statement True or False. Justify each answer.a. If $\mathbf{y}=c_{1} \mathbf{v}_{1}+c_{2} \mathbf{v}_{2}+c_{3} \mathbf{v}_{3}$ and $c_{1}+c_{2}+c_{3}=1,$ then $\mathbf{y}$ is a convex combination of $\mathbf{v}_{1}, \mathbf{v}_{2},$ and $\mathbf{v}_{3}$ .b. If $S$ is a nonempty set, then conv $S$ contains some points that are not in $S$ .c. If $S$ and $T$ are convex sets, then $S \cup T$ is also convex.

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Calculus 3

Chapter 8

The Geometry of Vector Spaces

Section 3

Convex Combinations

Vectors

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Lectures

02:56

In mathematics, a vector (…

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Mark each statement True o…

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In Exercises 16 and $17,$ …

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If $c \in \mathbb{R}$ and …

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In Exercises 11 and $12,$ …

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If $A$ and $B$ are convex …

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Tell whether each of the f…

05:16

Let $\mathbf{v}$ be an ele…

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In Exercises 21 and $22,$ …

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and this exercise statement a is false. We also need that every c I is a non negative number. Yeah, a statement fee is also false In the case when we Onley have one vector and its convex hole is itself a statement See, he's also false Consider the following example and are too Every line segment is a convex set. Thio is anti in this case our comeback sets on their union is not a comeback set. If it were comebacks, the it won't contain the following green segment, but it doesn't.

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If $A$ and $B$ are convex sets, prove that $A+B$ is convex.

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[M] Compute an SVD of each matrix. Report the final matrix entries accurate …

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In Exercises 5 and $6,$ let $\mathbf{b}_{1}=\left[\begin{array}{l}{2} \\ {1}…

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$[\mathbf{M}]$ In Exercises $14-17,$ follow the instructions given for Exerc…

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