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:

Subjectivist Fallacy

A logical error where one asserts that something is true or good merely because it is true or good for someone, ignoring any objective standards.

Contradiction

A relation between two or more statements that have opposite truth values for every assignment of truth values to their atomic components.

Subjectivism

The philosophical stance that knowledge and value are dependent on and limited by individual perception and experience.

Superstitious Robot

A hypothetical or fictional robot that acts or makes decisions based on superstitious beliefs rather than logical or rational processes.