Question

Determine if the subset of R^4 consisting of vectors of the form [a; 5a + b; -3a + 0b; 1a - 1b] is a subspace. Select true or false for each statement. 1. The set contains the zero vector 2. This set is closed under scalar multiplications 3. This set is a subspace 4. This set is closed under vector addition

          Determine if the subset of R^4 consisting of vectors of the form [a; 5a + b; -3a + 0b; 1a - 1b] is a subspace.
Select true or false for each statement.
1. The set contains the zero vector
2. This set is closed under scalar multiplications
3. This set is a subspace
4. This set is closed under vector addition

Determine if the subset of R^4 consisting of vectors of the form [a; 5a + b; -3a + 0b; 1a - 1b] is a subspace.
Select true or false for each statement.
1. The set contains the zero vector
2. This set is closed under scalar multiplications
3. This set is a subspace
4. This set is closed under vector addition

Added by Jennifer M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

03/29/2023

Step 1

The set contains the zero vector: To check if the set contains the zero vector, we need to see if there exists a and b such that the vector is (0, 0, 0, 0). (5a, b, -3a, -b) = (0, 0, 0, 0) This is true when a = 0 and b = 0. So, the set contains the zero vector. Show more…

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Determine if the subset of R^4 consisting of vectors of the form [a; 5a + b; -3a + 0b; 1a - 1b] is a subspace. Select true or false for each statement. 1. The set contains the zero vector 2. This set is closed under scalar multiplications 3. This set is a subspace 4. This set is closed under vector addition