Determine which of the following subsets of R^n are in fact subspaces of R^n (n > 2). (a) {x | x_1 >= 0}, (b) {x | x_1 = 0}, (c) {x | x_1x_2 = 0}, (d) {x | sum_{j=1}^n x_j = 0}, (e) {x | sum_{j=1}^n x_j = 1}, (f) {x | Ax = b, where A_{mxn} != 0 and b_{mx1} != 0}.
Added by Kyle M.
Close
Step 1
To determine if this is a subspace, we need to check if it satisfies the three conditions for a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector. - Closure under addition: Let x and y be two vectors in the Show moreā¦
Show all steps
Your feedback will help us improve your experience
Sri K and 86 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Which of the following are subspaces (mark all that apply)? let A be an m x n matrix and v1, v2, v3 be vectors in R^n a) The set of vectors x in R^n such that Ax =0 b) The set of vectors x in R^n such that Ax = b c) The span of the columns of A d) All the possible combinations of v1, v2, v3 e) [x y z] = t [ 1 -1 1] f) [x y z] = [3 -1 1] + t [3 2 1] + s[1 0 -1]
Vincenzo Z.
Determine which of the following subsets of Rn are in fact subspaces of Rn (n > 2). If it doesn't satisfy the question, please write down the reason. a) {x | x = 2, 0} - False b) {x | x = 0} - True c) {x | x, z != 0} - False d) {x | Is - x = 0} - False e) {x | Ix; -, x; = 1} - False f) {x | Ax = b, where A != 0 and b != 0} - True
Prakriti R.
Determine whether the following sets are subspaces of R4: a) All vectors x in R4 such that Ax = [0; 1], where A = [0 -1 0 2; -1 1 0 1]. b) All vectors of the form (a, a + 1, 0, a3).
Shu-Ting H.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD