1 V₁ = 2 - Copyright Texas State University, 2 3 rights reserved. V₂ = University, 2023 1 1 V3 = Copyright Texas State University, 2023. All rights reserved. 2 [1] a. Determine if b is in Span(V1, V2, V3)2State University, 202 Copyright Copyright 0 Copyright Texas State University, 2023. All rights reserved. b= ts reserved. This represents an exam for use only in Math 3377.301 S23. The material is written on a per-student basis and all material is protected by Copyright and property of Texas State University, 2023. All rights reserved. You may not copy, reproduce, distribute, publish, display, modify, create derivative works, transmit, or in any way exploit any such content, nor may you distribute any part of the content over of the examination is expressly any network, sell or offer it for sale, or use such content to construct any kind of database. You may not alter or remove any copyright or other notice from copies of the content. Copying or storing any content except as provided for the sole use prohibited without prior written permission. 2 1 e University, 2023. All rights reserved. b. Based on your row reduction in part (a), is {V₁, V2, V3} dependent or independent? Texas State University, 2023. All rights reserved. University, 2023. All rights reserved. Copyrigh Copyright c. Is b in the span of any subset of {V₁, V2, V3}? If "yes", which one. If "no", why not? iversity, 2023. All rights reserved. 2023. All rights reserved. 2023. All rights reserved.

4. Determine if the vectors are orthogonal, in the same direction, or neither. Briefly explain your reasoning. -> v = (4, – 15, - 2> 1 1 3'4'6

Use the given vectors to answer the following questions. a=(4, 2, 2), b = (-1, 1, 0), b = (-1, 1, 0), c = (0, 0, -5) (a) Find a x (b × c). ax (bx c) = (b) Find (a x b) x c. (a x b) x c = Need Help? Read It

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Find the magnitude of the following vector. (-1, 2)

Pls help on this.

V u Write the vector shown below as a combination of vectors and shown above Vector = 2 Xu + 3 xv Note: In both graphs, each box is 1 unit by 1 unit in size

Consider the following vectors: 1 ·1 3 a =-2 -3 b= = = 0 -8 -3 For each of the following vectors, determine whether it can be written as a linear combination of these vectors. If so, give the linear combination using the vector names above. 8 V1= 1 0 -3 V2=9 0 2 V3= II

Cross products of vectors