-1 --0----0 Let a₁ = 1 = -1 Is b a linear combination of a₁ and a2? 3 6 and 6 = Yes, b is a linear combination of a1 and a2. Ob is not a linaer combination of a₁ and 2. We cannot tell if b is a linear combination of a₁ and 2. Either fill in the coefficients of the vector equation, or enter "DNE" if no solution is possible. 6 = -.5 xa₁ + -2.5 x a₂ Check Answer
-1 --0----0 Let a₁ = 1 = -1 Is b a linear combination of a₁ and a2? 3 6 and 6 = Yes, b is a linear combination of a1 and a2. Ob is not a linaer combination of a₁ and 2. We cannot tell if b is a linear combination of a₁ and 2. Either fill in the coefficients of the vector equation, or enter "DNE" if no solution is possible. 6 = -.5 xa₁ + -2.5 x a₂ Check Answer
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Let \(\vec{a_1} = \begin{bmatrix} 3 \\ 1 \\ 6 \end{bmatrix}\), \(\vec{a_2} = \begin{bmatrix} -1 \\ -1 \\ -3 \end{bmatrix}\), and \(\vec{b} = \begin{bmatrix} 1 \\ 2 \\ 4 \end{bmatrix}\).
**Is \(\vec{b}\) a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\)?**
- ⬜ Yes, \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
- ⬜ \(\vec{b}\) is not a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
- ⬜ We cannot tell if \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
**Either fill in the coefficients of the vector equation, or enter "DNE" if no solution is possible.**
\[
\vec{b} =
\begin{bmatrix} -0.5 \end{bmatrix} \times \vec{a_1} + \begin{bmatrix} -2.5 \end{bmatrix} \times \vec{a_2}
\]
\[ \text{Check Answer} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a99bde-e99a-4ca5-bad3-91849c93fae5%2Fd605fe4a-ca70-4e9a-bae5-3e9e8122fc6f%2Fg1eyww_processed.png&w=3840&q=75)
Transcribed Image Text:Let \(\vec{a_1} = \begin{bmatrix} 3 \\ 1 \\ 6 \end{bmatrix}\), \(\vec{a_2} = \begin{bmatrix} -1 \\ -1 \\ -3 \end{bmatrix}\), and \(\vec{b} = \begin{bmatrix} 1 \\ 2 \\ 4 \end{bmatrix}\).
**Is \(\vec{b}\) a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\)?**
- ⬜ Yes, \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
- ⬜ \(\vec{b}\) is not a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
- ⬜ We cannot tell if \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
**Either fill in the coefficients of the vector equation, or enter "DNE" if no solution is possible.**
\[
\vec{b} =
\begin{bmatrix} -0.5 \end{bmatrix} \times \vec{a_1} + \begin{bmatrix} -2.5 \end{bmatrix} \times \vec{a_2}
\]
\[ \text{Check Answer} \]
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