Determine If the Vector U Is in the Column Space

question 35

Multiple Choice

Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
-Let $\mathbf { v } _ { \mathbf { 1 } } = \left[ \begin{array} { l } - 4 \\ - 1 \\ - 2 \end{array} \right] , \mathbf { v } _ { \mathbf { 2 } } = \left[ \begin{array} { r } - 3 \\ 1 \\ - 2 \end{array} \right] , \mathbf { v } _ { \mathbf { 3 } } = \left[ \begin{array} { r } 1 \\ - 5 \\ 2 \end{array} \right]$ , and $\mathrm { H } = \operatorname { Span } \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\}$ .
Note that $\mathbf { v } _ { 3 } = 2 \mathbf { v } _ { 1 } - 3 \mathbf { v } _ { 2 }$ . Which of the following sets form a basis for the subspace $H$ , i.e., which sets form an efficient spanning set containing no unnecessary vectors?
$A : \left\{ v _ { 1 } , v _ { 2 } , v _ { 3 } \right\}$
$B : \left\{ v _ { 1 } , v _ { 2 } \right\}$
$C : \left\{ v _ { 1 } , v _ { 3 } \right\}$
D: $\left\{ v _ { 2 } , v _ { 3 } \right\}$

• A) B only
• B) A only
• C) B, C, and D
• D) \(B\) and \(C\)

Comprehend the relationship between educational level, gender, and patterns of alcohol consumption.

Identify and understand the pattern between alcohol consumption and mortality rates revealing the health implications of varying drinking behaviors.

Understand the biological and physiological effects of alcohol consumption.

Recognize the social and behavioral consequences of alcohol use.

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