The Given Set Is a Basis for a Subspace W

question 19

Multiple Choice

The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W.
-Let $\mathrm { x } _ { 1 } = \left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \mathrm { x } _ { 2 } = \left[ \begin{array} { r } 1 \\ 1 \\ - 1 \\ - 1 \end{array} \right] , \mathrm { x } _ { 3 } = \left[ \begin{array} { l } 1 \\ 0 \\ 1 \\ 1 \end{array} \right]$

• A) \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ 4 \\ - 4 \\ - 2 \end{array} \right] , \left[ \begin{array} { r } 18 \\ 4 \\ 19 \\ 13 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 0 \\ 0 \\ - 2 \end{array} \right] , \left[ \begin{array} { l } 6 \\ 0 \\ 1 \\ 3 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 1 \\ - 1 \\ - 1 \end{array} \right] , \left[ \begin{array} { l } 1 \\ 0 \\ 1 \\ 1 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ 2 \\ - 2 \\ - 4 \end{array} \right] , \left[ \begin{array} { r } 14 \\ 2 \\ 9 \\ 7 \end{array} \right]\)

---

Definitions:

Visual Vocabulary

The set of elements used by artists to communicate ideas, emotions, and narratives through visual means, including line, color, shape, and texture.

Income Inequality

The unequal distribution of household or individual income across the various participants in an economy.

Developed Countries

Nations with relatively high levels of economic growth and security, characterized by stable governments, a high standard of living, and access to healthcare and education.

Unequal Income Distribution

A situation where income is distributed unevenly among a population, leading to disparities in wealth and living standards.