Determine if the following sets are subspaces. Explain your answer 1. The unit disk in R2,...
Determine if the given sets are subspaces of R^3. Please show
work.
3. (2 points) Determine if the given sets are subspaces of R3. -- (a) Wi 1 = :u2= 1 u2 u3 nt s { (b) Wi u3= 3u1 + u2 u2 | U3 4 4. (3 points) If A find A100 by diagonalizing A. 2
3. (2 points) Determine if the given sets are subspaces of R3. -- (a) Wi 1 = :u2= 1 u2 u3 nt s...
Determine which of the following sets are subspaces of the given vector space. If it is NOT a subspace, circle NO and give a property that fails. Circle YES if it is a subspace, but you do NOT have to prove it. Let a and b be real numbers. a a+b (b) Let S= 1 . Is S a subspace of R3? YES or NO (c) Let S = {p(t) |p(t) = at + bt}. Is S a subspace of...
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
5. (a) (7 marks) Determine whether the following sets form a basis for R3. Explain your answers. i. - {0:0} - {0:00) - {000) -*-**(0-1 1 (b) (3 marks) Is the set W = a vector space? Explain your answer.
part a and b
PROBLEM (HAND-IN ASSIGNMENT) Use the Subspace Test to determine whether the following sets W are subspaces of the given vector spaces: (A) The set W to be of all triples of real numbers (x, y, z) satisfying that 2x - 3y + 5z = 0 with the standard operations on Ris a subspace of R3. (B) The set of all 2 x 2 invertible matrices with the standard matrix addition and scalar multiplication.
Question 2. 20 marks Determine whether the following sets form subspaces of the standard 2-dimensional Euclidean space (R%. +. :): (a) A = {(11.12)|*1 = -2). (b) B = {(21,12) 2119 = 0). (e) C = {(1, 12) 12 = 2x;}. (d) D = {(2,12) ||*|-|-2), where x. denotes the absolute value of x, for i=1,2. (e) E = {(*1,22) | } = =3)
1. Determine whether each of the subsets below are subspaces of R3. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the x, y plane two units above the origin.
2. Determine which of the following are subspaces of R3: (a) all vectors of the form (a,b,c)), where a - 2b = c. (b) all vectors of the form (a, b, -3)), (c) all vectors of the form (a, b,0)). Explain your answer.
(1 point) Are the following statements true or false? False 1.If S and S2 are subspaces of R" of the same dimension, then Si -S2 False 2. If the set of vectors U spans a subspace S and U is not already a basis for S, thein vectors can be added to U to create a basis for S False 3. Three nonzero vectors that lie in a plane in R3 might form a basis for R3 False 4. If...
4. A random point (X, Y ) is chosen uniformly from within the unit disk in R2, {(x, y)|x2+y2< 1} (a) Let (R, O) denote the polar coordinates of the point (X,Y). Find the joint p.d.f. of R and . Compute the covariance between R and 0. Are R and e are independent? (b) Find E(XI{Y > 0}) and E(Y|{Y > 0}) (c) Compute the covariance between X and Y, Cov(X,Y). Are X and Y are independent?
4. A random...