Suppose we wish to find the coordinate vector of w = -31 4 3 -1 relative to the basis S = { [10]-3 1. What system of equations must be solved to find that vector? 2. And what is (w)s = W1 + W1 W₂ W2 = || =
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![Suppose we wish to find the coordinate vector of w =
-31
4
3
-1
relative to the basis S = {
[10]-3
1. What system of equations must be solved to find that vector?
2. And what is
(w)s =
W1
+
W1
W₂
W2
=
||
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2Fc97ae4e7-6dc9-45e0-9e9d-03d486e1d721%2Fvpz77v7_processed.jpeg&w=3840&q=75)
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- Find the vector X (in standard coordinates) determined by the given coordinate vector [X] B and the given basis B. 3 -2 {³}]} =[3³] B - 5 Enter the answer only (don't type your work here), using the equation editor. B =4. (a) Determine if the four points P1: (1,1,- 2), P2: (4,0,- 3) P3 :(1,-5,10), and P4 : (-7,2, 4) lie on the same plane. (b)Two vectors are parallel if and only if they are nonzero scalar multiple of each other's. Find a vector ( b )that is parallel to a = 3i + 7j and has magnitude 2.Suppose the polynomial ax² + bx + c corresponds to the vector (a, b, c). 2 To what polynomial will (3,4,2) correspond? 3x+4x+2 2 To what polynomial will (3, -3, -5) correspond? 3x²-3x-5 To what polynomial should (3, 4, 2) + (3, -3, -5) correspond? 6x+x-3 What should the corresponding vector be? (6,1,-3) vector components) 2 To what polynomial should 2(3,4,2) correspond? 6x²+8x+4 J What should the corresponding vector be? (6,8,4) Submit Question A Part 2 of 5 Part 3 of 5 (Use to enclose the ▼ Part 4 of 5 Part 5 of 5 Based on the preceding, is there any significance to the componentwise sum of two vectors?" Defend your conclusion..
- A line contains the points P=(−6,−2,−3)P=(-6,-2,-3) and Q=(−4,−3,−6)Q=(-4,-3,-6). A vector equation of this line is →x=−−→OP+t−−→PQx→=OP→+tPQ→, where OO is the origin.If t=2t=2, what point does this give us from the equation?If possible, find a linear combination of the form w = a₁v₁ + a₂₂ + 3⁄³ where v₁ = (2, −1, 4), v₂ = (3, 0, 1), v3 = (1, 2, −1), and w = (-7, 1, 5). (Give a, a, and a3 as real numbers. If w cannot be written as a linear combination of the other three vectors, enter DNE.) (₁₁²₂₁²3) =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)
- 10. (a) The non-zero vectors a, b andc are such that axb exa. Given that b -e, find a linear relationship between a, b and c. (b) The variable vector v satisfies the equation vx(i-3k)= 2j. Find the set of vectors v and [(b) v = HER] fully describe this set geometrically.Which equations below represent the line in R³ that passes through the point (-3,5,-5) and is parallel to the vector 3i + 4j + 6k? You may select more than one equation. Or(t): +t OF(t) = + t Ox=3+3t; y = 5 + 4t; z = = 5 + 6t - OF(t): = -3, 5, -5> +t OF(t) = +t 1 - x=3+ 6t; y = 5 + 8t; z = 5+ 6t OF(t)= +t OF(t)= + t -Suppose the straight lines L₁ and L₂ have respective vector equations 5 r1 = -3 + t -0-0--0- and 4 3 where s and t are scalar parameters. 9 = 8 +s -2 -5 -5 2 a) Given that L₁ and L2 intersect at some point P, find its coordinates. P =( )
- Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true. Jū+ ☐ v+ ☐ w = ō.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 26isto 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.
