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)
• \[
• \left\{\left[\begin{array}{l}
• 2 \\
• 1 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{c}
• \frac{29}{3} \\
• 0 \\
• -\frac{4}{3} \\
• 1
• \end{array}\right]\right\}
• \]

---

Definitions:

Belongingness

An emotional need or desire for strong and stable relationships with different groups or communities.

Self-Esteem

An individual's overall subjective emotional evaluation of their own worth or value.

Self-Compassion

Being kind to yourself; treating yourself with the same sense of compassion that you would treat others.

Self-Kindness

Treating oneself with understanding and forgiveness, recognizing one's own needs and nurturing one’s wellbeing.