Find a Basis for the Column Space of the Matrix $\mathrm { P } _ { 7 }$

question 24

Multiple Choice

Find a basis for the column space of the matrix.
-Determine which of the following statements is false.
A: The dimension of the vector space $\mathrm { P } _ { 7 }$ of polynomials is 8 .
$B$ : Any line in $R ^ { 3 }$ is a one-dimensional subspace of $R ^ { 3 }$ .
$C :$ If a vector space $\mathrm { V }$ has a basis $B = \left\{ b _ { 1 } , \ldots . . , b _ { 7 } \right\}$ , then any set in $\mathrm { V }$ containing 8 vectors must be linearly dependent.

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

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Definitions:

Marginal Cost

The cost added by producing one additional unit of a product or service, a critical factor in economic decision-making.

Society's Welfare

The overall well-being and standard of living of the community or society as a whole.

Marginal Cost

An additional cost incurred for producing one more unit of a product.

Marginal Social Benefit

The additional benefit to society from consuming one more unit of a good.