Question

Determine if the subset of (mathbb{R}^3) consisting of vectors of the form (egin{bmatrix} a \ b \ c end{bmatrix}), where (abc = 0) 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 closed under vector addition 4. This set is a subspace

          Determine if the subset of (mathbb{R}^3) consisting of vectors of the form (egin{bmatrix} a \ b \ c end{bmatrix}), where (abc = 0) 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 closed under vector addition
4. This set is a subspace

Determine if the subset of (mathbbR^3) consisting of vectors of the form (eginbmatrix a b c endbmatrix), where (abc = 0) 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 closed under vector addition
4. This set is a subspace

Added by Amanda B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Vysakh M

Step 1

- The zero vector in \(\mathbb{R}^3\) is \(\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}\). - For this vector, \(abc = 0 \cdot 0 \cdot 0 = 0\). - Therefore, the zero vector is in the set. - Statement 1 is True. Show more…

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Determine if the subset of R^3 consisting of vectors of the form [a; b; c], where abc = 0 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 closed under vector addition 4. This set is a subspace