Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)S = {(2, -1, 3), (5, 0, 4)}(a)z = (3, -4, 8)Z =S1 +S2ca) v- (10, - 4)59(b)V =V =S1 +(c)W =(8, -9, 19)W =S1 +(d)u = (3, 1, -1)», + (u =S1S2

Given : The given set is S = {(2, -1, 3) , (5, 0, 4)}. To find : We have to write the following…

Answered: Write each vector as a linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let a₁ = -4, a₂ = 3 and b = " Is b a linear combination of a₁ and a₂? OA. b is not a linear combination. B. Yes b is a linear combination. C. We cannot tell if b is a linear combination. b= -7 -B -13 -8 Either fill in the coefficients of the vector equation, or enter "NONE" if no solution is possible. a₁+ a2
Let Are the vectors 7₁, 72 and 3 linearly independent? linearly dependent If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. -O]++] 1 26 V₁ = = [3₁]. * = [9] = [²6]- ₁ V3 26
isto 5 4 3 2 - 4c = < 1 5 -4 -3 -2 -1 -1 -2 wŃ -3 -4 1 2 3 4 Find the components of the vector -4c based on the vector shown.
Let -0-0-0-0 V2 = w= -5 = -2 = = If possible, express w as a linear combination of the vectors V₁, V2 and v3. Otherwise, enter DNE. For example, the answer w = 4v₁ + 5v2 + 603 would be entered 4v1 + 5v2 + 6v3.
1. Suppose a and bare vectors such that a x b = (1, 0, 2). What is bx -2a *x (-2a² a. (-2, 0, -4) c. (1, 0, 2) d. (-4, 0, -2) b. (2,0,4)
Express the vector v =-1 as a linear combination of the vectors --3 V1 0,v2 4 and v3 -4 , if possible. Show all of the steps that you used %3D 3 -2 11 in obtaining your solution. 3.
The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)
How do you know if three vectors are on the same line? (when they are on the same line we call them co-linear) If when you add them up, you get a constant If they are the same. If they are different. If each is a multiple of the other one. If you multiply the first one by 7 you get the second one and when you multiply the second one by your age, you get the third one for sure.
The set containing the elements specified also possesses its relevant operations of multiplication over reals and vector addition. Is the set a real vector space?
Consider the following vectors: u = (1, −2, −1), v = (-2, 1, 8) Without using the cross product, find a vector n which is orthogonal to both u and U. You need to use a notion from chapter 5 to set up a system of linear equations, then use RREF to solve the system. Explain why this method works.
Assume v1 = [3,-2] and v2 = [-1,4]. Find the sum and difference of vectors v1 and v2. v1 + v2 = [Answer,Answer] v1 − v2 = [Answer,Answer]
Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1, -1,2) * 12- Find the distance of the following vectors: (a – d)² + (2c - b) = a² * (b-d+c) =

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Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, –1, 3), (5, 0, 4)} (a) z = (3, -4, 8) Z = S1 + - (18, - ) 59 (b) V = V = S1 + (c) w = (8, -9, 19) W3= S, + S2