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GO Classes | DA Course | Linear Algebra

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Inside of $\mathbb{R}^3$, consider the subset of vectors

$$
\left\{\mathbf{v}=\left[\begin{array}{c}
a \\
b \\
a
\end{array}\right]\right\}
$$

satisfying the following requirements. Which of them are subspaces?

  1. $a$ and $b$ are both zero.
  2. $a$ is any number and $b$ is zero.
  3. $a$ is zero or $b$ is zero or both are zero.
  4. $a, b$ are both positive, both negative, or both zero.

1 Answer

0 0 votes
Properties of subspace:

1.The zero vector is in the subspace

2.Subset is closed under addition and scalar multiplication

Option A,B,D satisfies these properties but option c is not closed under addition , for example

vector1=[1 0 1]^t  (where b=0) and vector2=[ 0 1 0 ]^t (where a=0).Their sum is [1 1 1 ]^t which does n't satisfy the condition a=0 or b=0 or both.
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