Let v1, v2, v3, w E R'. Let a2 a3 b2 be vectors in R³ satisfy b3 avi + azv2 + azvz = bịvi + bzv2 + bzvz = w. Set e = a1 – b1, c2 = a2 – b2, c3 = az – b3. a) Prove that C1v1 +Cz®2 + czV3 = 04. b) If d; = a; + te; for i = 1,2,3 and t any scalar, prove that div + dzv2 + dzv3 = w.

Q: Let S be the subset of R2 consisting of all vectors of the form (a, b + 3). a) Show that (5, 2),…

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A: We have given three non-zero vector.

Q: 5. Express u = (-4, 3, —2) using the unit vectors.

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Q: Find the inverse Laplace transform f (t) = L¯¹{F(s)}. 3 2s a. F(s): = - b. F(s): = 2s-5 s²-4s+13…

A: ​(a) L−1{F(s)}=23​e25t​−(34sin(3t)​+2cos(3t))e2t​​(b)L−1{F(s)}=−e−2t+tet+2et​Explanation:Step 1: a.…

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A: The given matrix is ;                     A =  577-10-311-86713914 If  C1 , C2 , C3  and  C4  are…

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A: Given that the vectors w=-146 , v1=5-4 ,  v2=-4-3 ,  v3=11 .

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Q: 4.) Are vectors Linearly independent? 2 3

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Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

A: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

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A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

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A: we will write the given vector as linear combination of vectors in as and find the unknown…

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A: The given differential equation is t2y''+4y'+5+ty = 0→1. The objective is to find the value of Wy1,…

Q: Let ~u = ( 1, -1, 0) and ~v = ( -1, 0, 1). Find ~u - ~v and ~u + ~v. b) Are the vectors ~u − ~v and…

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Q: Consider the vectors u = (-5, -9, 3) and v = (1, -9, 3). Determine u x v. A) (0, 19, 54) B) (0, 18,…

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Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from