Find a Basis for the Column Space of the Matrix $\mathrm { V }$

question 44

Multiple Choice

Find a basis for the column space of the matrix.
-Determine which of the following statements is true.
A: If $\mathrm { V }$ is a 4 -dimensional vector space, then any set of exactly 4 elements in $V$ is automatically a basis for $V$ .
B: If there exists a set $\left\{ \mathbf { v } _ { 1 } , \ldots \ldots , \mathbf { v } _ { 5 } \right\}$ that spans $V$ , then $\operatorname { dim } V = 5$ .
$\mathrm { C }$ : If $\mathrm { H }$ is a subspace of a finite-dimensional vector space $\mathrm { V }$ , then $\operatorname { dim } \mathrm { H } \leq \operatorname { dim } \mathrm { V }$ .

• A) \(A\) and \(C\)
• B) \(\mathrm { A }\)
• C) \(\mathrm { C }\)
• D) \(B\)

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