Let W Be the Subspace Spanned by the Uʹs A) $$\mathbf { y } = \left[ \begin{array} { r } 18 \\7 \\10\end{array} \right] + \left[ \begin{array} { r } - 1 \\4 \\- 1\end{array} \right]$$

question 26

Multiple Choice

Let W be the subspace spanned by the uʹs. Write y as the sum of a vector in W and a vector orthogonal to W.
- $$\mathbf { y } = \left[ \begin{array} { r } 19 \\3 \\11\end{array} \right] , \mathbf { u } _ { 1 } = \left[ \begin{array} { r } 1 \\0 \\- 1\end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { l } 2 \\1 \\2\end{array} \right]$$

• A)
• \[\mathbf { y } = \left[ \begin{array} { r }
• 18 \\
• 7 \\
• 10
• \end{array} \right] + \left[ \begin{array} { r }
• - 1 \\
• 4 \\
• - 1
• \end{array} \right]\]
• B)
• \(\mathbf { y } = \left[ \begin{array} { r } 13 \\ 0 \\ - 13 \end{array} \right] + \left[ \begin{array} { l } 6 \\ 3 \\ 6 \end{array} \right]\)
• C)
• \(\mathbf { y } = \left[ \begin{array} { r } 18 \\ 7 \\ 10 \end{array} \right] + \left[ \begin{array} { r } 1 \\ - 4 \\ 1 \end{array} \right]\)
• D)
• \(\mathbf { y } = \left[ \begin{array} { r } 18 \\ 7 \\ 10 \end{array} \right] + \left[ \begin{array} { l } 37 \\ 10 \\ 21 \end{array} \right]\)

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Definitions:

Diagnostic Systems

Structured methods used in healthcare and psychology to identify and classify diseases, disorders, and conditions based on symptoms and signs.

Reliability

The degree to which an assessment tool produces stable and consistent results over time.

Types of Reliability

Different ways of measuring the consistency of a test or research findings, including test-retest, inter-rater, and internal consistency reliability.

Diagnostic and Statistical Manual of Mental Disorders

A manual published by the American Psychiatric Association that provides a comprehensive classification and criteria for diagnosing mental disorders.