Find a Basis for the Column Space of the Matrix $$B = \left[ \begin{array} { r r r r } 1 & - 2 & 5 & - 3 \\2 & - 4 & 13 & - 2 \\- 3 & 6 & - 15 & 9\end{array} \right]$$

question 41

Multiple Choice

Find a basis for the column space of the matrix.
- $$B = \left[ \begin{array} { r r r r } 1 & - 2 & 5 & - 3 \\2 & - 4 & 13 & - 2 \\- 3 & 6 & - 15 & 9\end{array} \right]$$

• A)
• \[
• \left\{\left[\begin{array}{r}
• 1 \\
• 2 \\
• -3
• \end{array}\right],\left[\begin{array}{r}
• 5 \\
• 13 \\
• -15
• \end{array}\right]\right\}
• \]
• B) \[
• \left\{\left[\begin{array}{l}
• 1 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{l}
• 0 \\
• 1 \\
• 0
• \end{array}\right]\right\}
• \]
• C)
• \[
• \left\{\left[\begin{array}{r}
• 1 \\
• 2 \\
• -3
• \end{array}\right],\left[\begin{array}{r}
• -2 \\
• -4 \\
• 6
• \end{array}\right]\right\}
• \]
• D)
• \[
• \left\{\left[\begin{array}{l}
• 2 \\
• 1 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{c}
• \frac{29}{3} \\
• 0 \\
• -\frac{4}{3} \\
• 1
• \end{array}\right]\right\}
• \]

Recognize the importance of cultural competence in therapeutic practices.

Understand classical conditioning, operant conditioning, and their relevance to learning behaviors.

Describe the elements common to successful therapies and their significance in treatment.

Explain the concepts of internalized objects, modeling, observational learning, and their impacts on personal development and behavior.

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