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) \(B\)

---

Definitions:

Component Costs

The various expenses that make up the total cost of financing for a company, including the cost of debt and equity.

Market Values

The current price at which an asset or service can be bought or sold, determined by supply and demand.

Cost Of Debt

The effective rate that a company pays on its borrowed funds, which can include bonds, loans, and other forms of debt.

Flotation Costs

The expenses related to the release of new securities, encompassing fees for underwriting, legal services, and registration.