If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form u=w_1+w_2, where w_1 is a scalar multiple of v and w_2 is orthogonal to v. The vector w_1 is called the _____.

Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

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Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: Suppose V₁ = vector 1= Write five different vectors in Span{V₁, V2}. For each vector, show the…

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Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

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Q: 9. Show that is a two-dimensional vector. Ai = -x2 X1

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Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

Q: Need help with orthogonal vectors.

A: Step 1: Step 2: Step 3: Step 4:

Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: What if the vector v was [ 7, 11, 3]

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Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Find the length of the projection of 3   onto the vector -3…

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Q: Find a vector orthogonal to both ⟨1,−10,0⟩ and to ⟨0,7,4⟩ of the form

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Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

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Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Let be the vector with initial point (4, 7) and terminal point (8,4). Express as a linear…

A: The objective of this question is to express the vector v as a linear combination of the standard…

Q: Suppose and are vectors such that a × b =(3, 1, 4). What is the cross product of twice of a with…

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