If possible, find a linear combination of the form w = a₁v₁ + a₂V₂ + a3V3 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.) (a₁a₂₁ a3) =

Q: a (1, 0, 1), b = (2, 1, −1) and c = (1, -1, 4). Calculate |ax (b+c)].

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Q: Compute (3, -3,1) • (-1, -3, -4). (3, − 3,1) • ( − 1, − 3, -4)= (Simplify your answer.) - -

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Q: 15. Prove: If a, b, c, a, and M are constants and M = 0 then ax²y" + bxy' + cy has a particular…

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A: Step: 1 Linearly Dependent: - A set of vectors is called linearly dependent if at least one element…

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Q: Let u = 4u + 5v (9, -2, -8) and v = (4, −3, −1).

A: The required solution is:<56,-23,-37>Explanation:

Q: Show that fu,, u,) is an orthogonal basis for R?. Then express x as a linear combination of the u's.…

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Q: Suppose [V] B₁ [V] B₂ = 7 1 3 -[-]-* *, - {{; } [³])} and B₂ - {[²][³])}; [ 2 ] = find B₂ = If B₁ =…

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Q: Evaluate for r=(3,5) , s=(-6,4) , and t=(6,-1). 2r-(s+t)=

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Q: -5 4x If possible, write -5 - 4x - 2x² as a linear combination of 2 - x + x²,-2-x² and x - 5 2x².…

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Q: Suppose u=⟨−4,4,−2⟩ and v=⟨4,−2,3⟩. Then u×v=   v×u=

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Q: Do the points (1, 5, −7), (1, 7, −10), and (1, 8, −13) lie on the sameline?

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Q: Find a + b, 2a + 3b, lal, and la - b|. a = (4, –3), b = (-2, 5) a + b = (9,2) (2,9) 2a + 3b =

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Q: xdx = ? (ах + b)(сх + d)

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Q: Find u + v, 2v, u- v, and 3u - 2v. u = (1, -4, 2, 1), v = (0, 2, 2, 3) (a) u + v = (1, – 2,4,4) (b)…

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Q: Suppose A = (-1, –5, –7) and AB= (-5, 14, 4). Then В — (5,-70,-28) help (points)

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Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). - 2ü + 20 (-8,-12 - 20)

A: Given :-  u=<3,-4,-10>  v=<-7,-2,0>  To find:-  2u+2v