100941Let w71- - [¹²2]· ³¹₁ - [ ²2₂]- ³₂ - [¹4] and ¹ - [8]==[22]V2=73- 285Is w a linear combination of the vectors 7₁, 72 and 73?w is a linear combination of 7₁, 72 and 73w is not a linear combination of 71, 72 and 73If possible, write w as a linear combination of the vectors v₁, v2 and 73.If w is not a linear combination of the vectors 71, 72 and 73, type "DNE" in the boxes.W =Check All Partsv₁ +√₂ +V3

Answered: Image /qna-images/answer/e6bb8dfd-4156-4d86-870d-fb0ab0b766f5.jpg

Answered: 41 [2₂] [4] Is a linear combination of…

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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-15 -20 as a linear combination of the vectors 11 Q write -15 A 11 -20 = 1 1 -0·8·6 1 4. + + -2 A -2 1
Let 03 = If possible, express w as a linear combination of the vectors 1, 02 and 3. Otherwise, enter DNE. For example, the answer w = 401+502+603 would be entered 4v1 + 5v2 + 6v3. w =
Sho Express the following system of linear equations as a vector equation. 721+522-823= 5 6x1+2x2 + 2x3 = 5 -5x1 +52 + 223 = -3 8-8-8-8
2v1 +3V2 + V3 V4 +5V5 (V3 and V4 are multiplied) is a linear combination of the vectors V1, V2, V3, V4, V5. True O False
Find the image of the vector = (1, 2) by rotating it 30° counter-clockwise and scaling it by a factor of 4. Select all answers that are correct. O 2sqrt(3)-4 is the first component O 2+4sqrt(3) is the second component O 2sqrt(3)-4 is the second component O 2+4sqrt(3) is the first component none of these above
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]
3 -i Rewrite the vector v = in the form a + ib, where vectors a and b have only real components. 4 V2
a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =

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