a. Write the vector (23, -12, -19) as a linear combination of a₁ = (3, -2, -1),a2 (2, -3, -1) and ã3 = (-2, -2, 4). Express your answer in terms of the==named vectors. Your answer should be in the form 4ã₁ + 5ã2 + 6a3, whichwould be entered as 4a1 + 5a2 + 6a3.(23,-12,-19)b. Represent the vector (23, -12, -19) in terms of the ordered basisB={(3,-2,-1), (2, -3, -1), (-2, -2, 4)}. Your answer should be a vector ofthe general form <1,2,3>.[(23, 12, 19)] B =

Answered: Image /qna-images/answer/401ba5ec-5999-405b-aa4b-c0f4c3795ac8.jpg

Answered: a. Write the vector (23,-12, -19) as a…

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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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)
Given vector b = < -8, 10 > and vector p = < 1, 4 > find -6b + 3p
a, b, and c are vectors. Then the expression a×c+b×a is (a) Meaningless (b) A vector collinear with a (c) A vector orthogonal to a
Are the vectors -2-², 1+ 2x + x² and 2x - 2-2 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros 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. 0=(x-2-x²)+[ | (1 + 2x + x²)+ (2x − 2 − x²).
a, b and c are three vectors in the third dimension with the following properties: a × b does not equal zero. a × b = b × c = c × a. Show that a + b + c = 0. Show that a + b + c = 0.
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4, 1)} (a) u = (6, 25, -20, -3) J: + (3 u = -1 52 (b) -10, 2) 3 -- F1 + 4 52 2 (c) 57 w = -4, -14, -)- 7 13 4 = (14, -3, 7, (d) 41 z = b1 + $2
if given the equation yi = B0 + B1xi +ui and express the same equation as y = xiB = ui (where xi and B here are vectors), does vector xi = [1 x1] or xi = [x1] (row vector) and B vector (column vector) = [B0; B1]?
Express each column vector of AA as a linear combination of the ordered column vectors C₁, C2, and c3 of A. -6 A = 6 2 4 3 Enter first column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3: Enter second column as a linear combination of columns of A in terms of the vectors C₁, C2, and c3: Enter third column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3:
6. -2 Write -7 as a linear combination of the vectors 4 -1 一日一日一日 6. -2 -7 2 4
Express each column vector of BB as a linear combination of the column vectors c1, c2, and c3 of B. 4 -2 4 B = |0 1 4 5 6 5 Enter first column as a linear combination of columns of B in terms of the vectors c1, c2, and c3: Enter second column as a linear combination of columns of B in terms of the vectors c1, c2, and c3: Enter third column as a linear combination of columns of B in terms of the vectors c1, c2, and c3:
Write a vector equation 81-8181-81 y+ that is equivalent to the system of equations: -2x + 6y + 7z 2x +9y + 7% + Y x 4 = -9 6% = -6 = =
Find if the vector w = (-3,2,-6) can be expressed as a linear combination of the vectors V₁ = (-1,-f, m) and v₂ = (m, l.f). Write the vectors V₁ and V₂ clearly. f=6 m=0 I=8

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