Which of the following sets of vectors does not span R?? Select one: a. (1,3, 2),...
Which of the following sets does not span R '? Select one: 1.00 on [101 [01 [01. None of the above. Check
linear algebra- Linear independence Problems 1. Show that the following sets of vectors in R" are linearly dependent: U = (-1,2,4) and V = (5.-10,--20) in R. (b) U = (3,-1), V =(4,5) and W = (-4,7) in R2. 2. Are the following sets of vectors in R3 linearly independent or linearly dependent? Show work. (-3,0,4), (5,-1, 2) and (1, 1,3) (b) (-2,0,1), (3, 2,5), (6,-1,1) and (7,0,-2)
Which of the following vectors are perpendicular to the lines r=<0,1,1> + t<1,1,0> and r=<1,0,0>+t<0,1,1>? a) <0,0,1> b) <-1,0,0> c) <1,-1,1> d) <0,1,0>
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
How many of the following sets of quantum numbers n,l,m I are allowed for the hydrogen atom? (0) 1,0,0 (ii) 1,0,1 (iii) 1,1,0 (iv) 1,1,1 Select one: a. 4 b. none C. 3 d. 2 e. 1
(1 point) Select all of the vectors that are in the span of { ul , u2, u3 } . (Check every statement that is correct.) A. The vectoris in the span. 0 -3 B. The vector-52-7 2 is in the span C. The vector2 is in the span D. The vector -2 is in the span. E. All vectors in R3 are in the span. F The vector-70 is in the span. G. We cannot tell which vectors are...
(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...
Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0) Find T (2,-1,1). a) (10,0,2) b) (3,-2-1) c)(2,2,2) d) (-3,-2, -3)
Question 5: Multiple Choices Assume that vi,2,ig are vectors in R3. Let S span ,02,s and let A be the matrix whose columns are these vectors. Assume that 1 -1 1 0 0 0-3a +b-2c We can thus conclude that A. {6,6,6) is L1. B. The point (1,1 - 1) is in the span of (o,2,s) C. The nullity of A is 2 D. The rank of A is 3 E. B and C are both correct
Question 8 (1 point) Which of the following sets is equal to {1,3}? o {2x + 1 € Z1-3 < x² < 3} {x² + 1 € Z|XE Z and x < 2} . o {x E N | 2x + 1 <2} o {x? EN|0 < 2x +1 < 3} O None of the above Question 7 (1 point) Let Α = {a, b, c} and consider the equivalence relation R = {(a, 1), (b, b), (c, c), (c,...