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QULJTIUNIL Which of the following sets of vectors in M2x2 (the vector space are linearly independent?...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
please help thank you, (1 point) Which of the following sets of vectors are linearly independent? A. {( 10, -16), (-5, 8 )} B. {(-4, -7, 1, -8), (1, 3, 9, 7)} c.{(-2, -6)} D.{(1, 3), (-7, 1)} E.{(-9, 4), (0,0)} F.{(0,0)} G.{(-3, 7), (9,-4), (5,-8)} H.{(6, 1, -8), (1, 2, 5)} (1 point) Are the vectors and 10 28 linearly independent? 19 linearly dependent If they are linearly dependent, find scalars that are not all zero such that the...
Determine which of the sets of vectors is linearly independent. Determine whether the vectors x2 -1, x2 + x -2, and x2 + 3x + 2 are linearly independent or linearly dependent in P2. A) Linearly Dependent B) Linearly Independent
Problem #2: Which of the following sets of functions are linearly independent on the interval (-0, c.)? [2 marks] (i) f1(x) = x, f2(x) = 4x, 13(x) = = x2 +6 (ii) f1(x) = 2e2x, 12(x) = 4e4x, f3(x) = 8e8x (iii) f1(x) = 8sinx, 12(x) = 4cos 2x, f3(x) 9 (A) (i) and (iii) only (B) (iii) only (C) none of them (D) (ii) only (E) all of them (F) (i) only (G) (i) and (ii) only (H) (ii)...
Determine whether the given sets of vectors are linearly dependent on mearly independent. Be sure to explain your work 21 0 0 0 54 3 2 1
= 5. Determine if the following are linearly independent subsets: a) Determine whether or not vectors (1,-1,1,1), (3,0,1,1), (7,-1,2,1) form a linearly independent subset of R4. [1 01 To 27 -2 1] Let A= and C = . Do A, B, and C form 2 -1 -1 1 a linearly independent subset of M2x2? c) Determine if 5,x? – 6x,(3 – x)² form a linearly independent subset of F(-00,00). 6. Are the following bases? Why or why not. a) {(1,0,2),...
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
linear independence question 20. Let V1, V2, ...,Vn be linearly independent vectors in a vector space V. Show that V2,...,Vn cannot span V.
1. Determine whether or not the four vectors listed above are linearly independent or linearly dependent. If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds. (1 point) 13--3-3 Let vi = and V4 1-11 Linearly Dependent 1. Determine whether or not the four vectors listed above are linearly independent...
Let M1, M2 and M3 are linearly independent sets of vectors, and that M, C M, CM2. Let M = M, UM, U M3. Then, which of the following is always true? a) M is linearly dependent b) M is linearly independent c) M is both linearly dependent and linearly independent d) M is neither linearly dependent nor linearly independent