Determine which sets in Exercises 1-8 are bases for R3. Of the sets that are not...
(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...
2. (2 pts per part) Determine which sets are bases for R2 or Rs. Justify your answers. (No computations are needed here.) • {B} - {{!.]} {{H 11 0.
Determine whether the set of vectors is a basis for R3. Given the set of vectors decide which of the following statements is true: A: Set is linearly independent and spans R3. Set is a basis for R3. B: Set is linearly independent but does not span R3. Set is not a basis for R3. C: Set spans R3 but is not linearly independent. Set is not a basis for R3. D: Set is not linearly independent and does not...
Determine whether the following sets are linearly dependent or linearly indepen dent. If they are linearly dependent, find a subset that is linearly independent and has the same span (b) ((1,-1,2), (1,-2, 1), 1,4, 1)) in R3. (c) (1, 1,0), (1,0, 1), (0,1,1in (F2) (recall that F2-Z/2Z, the field with two elements).
Question 7 Determine whether the set of vectors is a basis for R? s{{JAMA}.d Given the set of vectors decide which of the following statements is true: A: Set is linearly independent and spans R. Set is a basis for R. B: Set is linearly independent but does not span R3. Set is not a basis for Rs. C: Set spans R but is not linearly independent. Set is not a basis for R. D: Set is not linearly independent...
3. [1 mark each] Determine which of the following statements are true and which are false. (a) The inverse of a rotation matrix (Rº) is (R-8). (b) If the vectors V1, V2, ..., Vk are such that no two of these vectors are scalar multiples of each other then they must form a linearly independent set. (c) The set containing just the zero vector, {0}, is a subspace of R”. (d) If v, w E R3 then span(v, w) must...
need help on this. Thanks in advance Question 7 Determine whether the set of vectors is a basis for R3. s{{JAMA). Given the set of vectors decide which of the following statements is true: A: Set is linearly independent and spans R. Set is a basis for R. B: Set is linearly independent but does not span R3. Set is not a basis for R. C: Set spans R3 but is not linearly independent. Set is not a basis for...
_Determine which of these sets is a basis for R3. 1 - 1 ^ {[:] 7] [8]} - {[7] | c{[7] [8] [8]} » {[![10]} Determine the dimension of the subspace W = span {V1, V2, V3, V4} where A. dim(W)=1 B. dim(W) = 2 C. dim(W) = 3 D. dim(W) = 4 8 Determine both the rank and nullity of the matrix A= [1 0 1 | 2 -3 4 -2 -2 2 -4 1 0 3 -4 2...
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
(i) Suppose L = {(1, 4, 2, 2),(2, 2, 1, 2),(2, 4, 2, 1)}. Is L linearly independent in R^4 ? Justify your answer. (ii) Suppose S = { 0 0 1 0 , 0 2 3 0 , 4 1 0 0 }. Is S linearly independent in M2(R)? Is span(S) = M2(R)? Justfy your answers.