Question

11. Which of the following are subspaces of $ R^{3} $ ? (i) $ \quad\{(2+a, b-a, b) \mid a, b \in R\} $ (ii) $ \quad\{(a+b, a, b) \mid a, b \in R\} $ (iii) $ \{(2 a+b, 0, a b) \mid a, b \in R\} $

          11. Which of the following are subspaces of \( R^{3} \) ?
(i) \( \quad\{(2+a, b-a, b) \mid a, b \in R\} \)
(ii) \( \quad\{(a+b, a, b) \mid a, b \in R\} \)
(iii) \( \{(2 a+b, 0, a b) \mid a, b \in R\} \)

$11. Which of the following are subspaces of R^3 ? (i) {(2+a, b-a, b) | a, b ∈ R} (ii) {(a+b, a, b) | a, b ∈ R} (iii) {(2 a+b, 0, a b) | a, b ∈ R}$

Added by Elizabeth A.

Linear Algebra and Its Applications

Gilbert Strang 4th Edition

Chapter 2

Instant Answer

Solved by Expert Aidan Mcnabb

01/02/2022

Step 1

A subset $V$ of $R^3$ is a subspace if it satisfies three conditions: - It contains the zero vector. - It is closed under vector addition. - It is closed under scalar multiplication. Show more…

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11. Which of the following are subspaces of $ R^{3} $ ? (i) $ \quad\{(2+a, b-a, b) \mid a, b \in R\} $ (ii) $ \quad\{(a+b, a, b) \mid a, b \in R\} $ (iii) $ \{(2 a+b, 0, a b) \mid a, b \in R\} $