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Problem #11: Let v1 = (-1,2,-1) and v2 = (-2,-1,-2). Which of the following vectors are...
Problem #7: Which of the following statements are always true for vectors in R3? (i) If u (vx w)-4 then w - (vxu)-4 (ii) (5u + v) x (1-40 =-21 (u x v) (ili) If u is orthogonal to v and w then u is also orthogonal to w | V + V W (A)( only (B) (iii) only (C) none of them (D) (i) and (iii) only (E) all of them (F) (i) only (G)i and (ii) only (H)...
Problem #3: According to the integral estimate, what is the smallest number of terms of the series n=1 that would have to be added in order to estimate its sum with an error that is less than .001? Problem #3: Just Save Submit Problem #3 for Grading Problem #3 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #4: Use the comparison test to determine which of the following series converge 00 7n 2 (i) 6P" (ii) n...
Please answer part a and b :) Which of the following vector fields are conservative? (i) F(x, y) = (9y8 +3) i + (8x8y' +7) j (ii) F(x,y) = (8ye8x + cos 3ji + (e8x + 3x sin 3jj (iii) F(x,y)-7y2e7xyİ + (7 +xy) e7xyj (A) all of them (B) (iii) only (C) (i) and (ii) only (D) (i) and (iii) only (E) none of them (F) (ii) and (iii) only (G) (ii) only (H) (i) only st Save Submit...
Please show work Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
Consider the following three vectors in ; v1 = (1, 7, −2), v2 = (4, 3, 5), v3 = (2, −11, 9): i) Say whether v1, v2, v3 are linearly dependent or linearly independent. (Justify) ii) Say if v1, v2, v3 generate . (justify) iii) If it exists, determine the constants c1, c2, c3, such that c1v1 + c2v2 + c3v3 = (0, −5, 13/5), or argue why it cannot be written as a linear combination. We were unable to...
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.
Problem #2: Let X be an exponentially distributed random variable with with 1 = . What is Var(X)? Problem #2: Just Save Submit Problem #2 for Grading Attempt #1 | Attempt #2 | Attempt #3 Attempt #4 Attempt #5 Problem #2 Your Answer: Your Mark:
(1 point) Suppose V1, V2, U3 is an orthogonal set of vectors in R. Let w be a vector in Span(V1, U2, U3) such that 01.01 = 33, U2 · U2 = 10.25, 03 · 03 = 36, W • V1 = 99, w · U2 = 71.75, w · Uz = -108, then w = Vi+ U2+ U3
2. Consider the vectors -11 -11] 31, ; [-9] 13 -2. V2 = V = 14 -51 3 V3 = 3 [-14] -12 16 16 V4 = ' Vs = (a) Find a subset of {v1, V2, V3, V4, Vs} that is linearly independent and contains as many vectors as possible. (b) Prove that your answer to (a) indeed gives a maximal independent subset by showing that your subset has the same span as the original set of vectors {V1,...