Express the Vector X as a Linear Combination of the Uʹs

question 42

Multiple Choice

Express the vector x as a linear combination of the uʹs.
- $\mathbf { u } _ { 1 } = \left[ \begin{array} { r } - 2 \\ 0 \\ 1 \end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { l } 3 \\ 5 \\ 6 \end{array} \right] , \mathbf { u } _ { 3 } = \left[ \begin{array} { r } - 2 \\ 6 \\ - 4 \end{array} \right] , \mathbf { x } = \left[ \begin{array} { r } 9 \\ 39 \\ - 2 \end{array} \right]$

• A) \(\mathbf { x } = 4 \mathbf { u } _ { 1 } + 6 \mathbf { u } _ { 2 } - 4 \mathbf { u } _ { 3 }\)
• B) \(\mathbf { x } = 4 \mathbf { u } _ { 1 } - 3 \mathbf { u } _ { 2 } - 4 \mathbf { u } _ { 3 }\)
• C) \(\mathbf { x } = - 8 \mathbf { u } _ { 1 } + 6 \mathbf { u } _ { 2 } + 8 \mathbf { u } _ { 3 }\)
• D) \(\mathbf { x } = - 4 \mathbf { u } _ { 1 } + 3 \mathbf { u } _ { 2 } + 4 \mathbf { u } _ { 3 }\)

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Definitions:

Test-retest Reliability

Describes the degree to which the results of the same test administered on two separate occasions to the same individuals remain consistent.

Percentile

A statistical measure indicating the value below which a given percentage of observations in a group of observations falls.

Normal Curve

A bell-shaped curve that represents the distribution of many types of data in which most values cluster around a central mean.

Standard Deviation

A statistic that measures the dispersion or variation from the average in a set of data, indicating how spread out the numbers are.