(1) Consider a collection of n individuals, each of whom owns a definite quantity of m commodities. Let aij be the number of commodity i owned by individual j. i = 1, 2, ...,m; j = 1, 2,..., n. What does the vector (a₁j, aj, ..., amj) represent? Explain in words the significance of the sum: (2) Evaluate A+ B, A- B, 5A- 3B where A = (3) Evaluate A. B where ail + ai2 + ... + ain. A = 0 1 -1 23 7 0 1 2 2 3 1 4 -1 6 and B = and B = 1 -1 5 3 2 1 0 -1 0

Q: 10. Let n > 2 be an integer and let V be the subset of F" consisting of vectors (x1,..., xn)…

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Q: Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

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Q: n+5 c) Let y= and u= Write y as sum of two orth ogon al vector s, one n+4 n-1 is Span (u) and one…

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Q: 15. Which of the following vectors in Rº, if any, are parallel to u = (-2, 1, 0, 3, 5, 1)? (a) (4,…

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Q: Find the regression sum of squares. y 17 23 45 66 37 - 89 45 23 26 67 A) Cannot be calculated as it…

A: Here,  y y-y (y-y)2 17 -27.56 759.5536 23 -21.56 464.8336 45 0.44 0.1936 66 21.44…

Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: Let S = {(0,1,0), (,0, ), (, 0, )}. The %3D set S is an orthonomal set of vectors. If u = (2, 2, 1),…

A: see below the answer  here we use the system of equation to find (u)S

Q: onil s 2 S = {v1,V2} = 4 5 7 8. a. Explain why S is linearly independent but is not a basis for R³.…

A: A basis for a subspace S of Rn is a set of vectors in S that is linearly independent and is maximal…

Q: Which of the following sets of vectors are linearly independent? (Check the boxes for linearly…

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Q: 0-0-0 2. 11 S = { %3D linearly dependent or linearly independent?

A: A set of vectors {v1, v2......vn} is said to be linearly independent if there exist scalars, such…

Q: 7. Let -3 6 -0--0-0-H [-] 8, V3 11 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are…

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Q: 19. Which of the vectors (A)–(C) in Figure 22 is equivalent to v – w? (A) (B) (C) FIGURE 22

A: The vectors substraction: (v-w)

Q: 1. Given a vector a=(3, - 2, 2), the magnitude of a is and the normalized vector of a is_

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Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: Determine whether b is in the column space of A. [-10 21 A = 5 8-10, b = 3 [-3-36 1. A

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Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: 8. Consider the vectors [11, 2, 0, 1, 0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]); [0, 1, 1, 1,…

A: Remark: If no column (row) of a matrix can be written as linear combination of other columns (rows)…

Q: -1 A-34] 1 Let A = 5 Find vectors X1, X2,. X; so that N (A) equals span {x₁, x2,...,xj}. ..y

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Q: Let S be a set of linearly dependent vectors in R". Select the best statement. A. The set S cannot…

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Q: 5. Consider a vector va Could we write this equivalently as va

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Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: 5. For which value of x do the following vectors form a linearly dependent set in R -1 y =|x, in- х,

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Q: Assume m₁ = [4., 1.5] and m₂ = [1.5, 0.5] represent the mean vectors of pattern class 1 and class 2,…

A: To find the decision boundary between two classes, we need to find the equation of the line that…

Q: . The distance of a point in the 3-D system from the origin a. is defined by the absolute value of…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: Let u = and v = . Now, w = is a linear combination of i and v. That is, w = aju + azv. Determine…

A: Answer:

Q: 13) Check whether the following set of vectors are linearly dependent: ủ1 = (1,2,3), ủz = (1,0,1) ,…

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Q: How many students were included in the collection?

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Q: 1. Determine the linearly independent vectors of the following set. Show the steps for your result.…

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Q: Normalize the vectors a ---4:0

A: Here we have to normalize the vectors a and u.

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: 9. Determine whether the set of vectors i (2,-1), (3,-2), (0, 1)} basis for TR? is

A: We will check whether the given set of vectors is a basis of R2 or not.

Q: Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

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Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: 7 Let a and b be vectors in R" such that ||a||=||b||=2 and (a,b) = 1. Then ||ab||= ...

A: Let a and b be vectors in ℝn such that  a=b=2 and <a,b>=72 . Then we have to find the value of…

Q: 17.) If S= [(2, 2, 0), (2,-2, 0), (0, 0, 2)], find the set T of vectors that are the normalizations…

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