Question

Determine which of the following subsets of R^n are in fact subspaces of R^n (n > 2). If it doesn't satisfy the question, please write down the reason. a) {x|xi ? 0} Ture b) {x|x1 = 0} Ture c) {x|x1x2 = 0} False d) {x|?j=1 to n xj = 0} e) {x|?j=1 to n xj = 1} f) {x|Ax = b, where Am×n ? 0 and bn ? 0}

          Determine which of the following subsets of R^n are in fact subspaces of R^n (n > 2). If it doesn't satisfy the question, please write down the reason.
a) {x|xi ? 0} Ture
b) {x|x1 = 0} Ture
c) {x|x1x2 = 0} False
d) {x|?j=1 to n xj = 0}
e) {x|?j=1 to n xj = 1}
f) {x|Ax = b, where Am×n ? 0 and bn ? 0}

Determine which of the following subsets of R^n are in fact subspaces of R^n (n > 2). If it doesn't satisfy the question, please write down the reason.
a) x|xi ? 0 Ture
b) x|x1 = 0 Ture
c) x|x1x2 = 0 False
d) x|?j=1 to n xj = 0
e) x|?j=1 to n xj = 1
f) x|Ax = b, where Am×n ? 0 and bn ? 0

Added by Jennifer B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Prakriti R

02/22/2022

Step 1

In order for a subset to be a subspace, it must contain the zero vector. Since this subset does not contain the zero vector, it is not a subspace. b) {x | x = 0} - True This subset only contains one vector, which is the zero vector (0, 0, ..., 0). The zero vector Show more…

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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