Contex Bb 15432 X C For th x X 52°F Clear MyOp Муор х M MyOp x ← → CO https://www.myopenmath.com/assess2/?cid=201973&aid=14298454#/skip/12 Present Perfect Pro... Activities for ESL St. YouTube to Mp3 C... Admissions M Gmail Check Answer Matrix X Let a₁ = [], ā₂ = [6]. Is b a linear combination of a₁ and a₂? a₁+| (8) Wex and b = الأخبار - خرائط f Gmail - YouTube 2 Google YouTube [78] 93 (8) Fin X We cannot tell if b is a linear combination of a₁ and 2. Yes, b is a linear combination of a₁ and 2. Ob is not a linaer combination of a₁ and 2. My Q X H a2 Enter an integer or decimal number [more..] Q Search Either x Either fill in the coefficients of the vector equation, or enter "DNE" if no solution is possible. ME | Cheg x File sharing and sto... Maps Maps (3 poi Xx If the X Solve X M Sent X (8) Exx ES day day Translate News Deb Scott's 50 Stor AP Adblock Plus has b... Listening Test #2 ^G 40
Contex Bb 15432 X C For th x X 52°F Clear MyOp Муор х M MyOp x ← → CO https://www.myopenmath.com/assess2/?cid=201973&aid=14298454#/skip/12 Present Perfect Pro... Activities for ESL St. YouTube to Mp3 C... Admissions M Gmail Check Answer Matrix X Let a₁ = [], ā₂ = [6]. Is b a linear combination of a₁ and a₂? a₁+| (8) Wex and b = الأخبار - خرائط f Gmail - YouTube 2 Google YouTube [78] 93 (8) Fin X We cannot tell if b is a linear combination of a₁ and 2. Yes, b is a linear combination of a₁ and 2. Ob is not a linaer combination of a₁ and 2. My Q X H a2 Enter an integer or decimal number [more..] Q Search Either x Either fill in the coefficients of the vector equation, or enter "DNE" if no solution is possible. ME | Cheg x File sharing and sto... Maps Maps (3 poi Xx If the X Solve X M Sent X (8) Exx ES day day Translate News Deb Scott's 50 Stor AP Adblock Plus has b... Listening Test #2 ^G 40
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
![**Linear Combination of Vectors**
*Problem Statement:*
Given the vectors:
\[
\vec{a_1} = \begin{bmatrix} -4 \\ 9 \end{bmatrix}, \quad \vec{a_2} = \begin{bmatrix} 6 \\ 6 \end{bmatrix}, \quad \vec{b} = \begin{bmatrix} 78 \\ 93 \end{bmatrix}.
\]
**Question:** Is \(\vec{b}\) a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\)?
- We are asked to determine whether \(\vec{b}\) can be expressed as a combination of the vectors \(\vec{a_1}\) and \(\vec{a_2}\).
*Options:*
1. We cannot tell if \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
2. **Yes,** \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\). (This option is selected)
3. \(\vec{b}\) is not a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
- A check mark confirms that option 2 is the correct answer.
*Solution:*
To express \(\vec{b}\) as a linear combination, find coefficients \(c_1\) and \(c_2\) such that:
\[
\vec{b} = c_1 \vec{a_1} + c_2 \vec{a_2}
\]
*Input Section:*
- Enter the coefficients in the provided input boxes for \(c_1\) and \(c_2\), or type "DNE" if no solution exists.
\[
\vec{b} = \_\_ \, \vec{a_1} + \_\_ \, \vec{a_2}
\]
Click "Check Answer" after filling in the coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18574973-f25e-4ab8-b7d6-6007b5b87fc4%2F262a0770-af8d-4133-9f96-a4365acbb982%2Fmc4w5p_processed.png&w=3840&q=75)
Transcribed Image Text:**Linear Combination of Vectors**
*Problem Statement:*
Given the vectors:
\[
\vec{a_1} = \begin{bmatrix} -4 \\ 9 \end{bmatrix}, \quad \vec{a_2} = \begin{bmatrix} 6 \\ 6 \end{bmatrix}, \quad \vec{b} = \begin{bmatrix} 78 \\ 93 \end{bmatrix}.
\]
**Question:** Is \(\vec{b}\) a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\)?
- We are asked to determine whether \(\vec{b}\) can be expressed as a combination of the vectors \(\vec{a_1}\) and \(\vec{a_2}\).
*Options:*
1. We cannot tell if \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
2. **Yes,** \(\vec{b}\) is a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\). (This option is selected)
3. \(\vec{b}\) is not a linear combination of \(\vec{a_1}\) and \(\vec{a_2}\).
- A check mark confirms that option 2 is the correct answer.
*Solution:*
To express \(\vec{b}\) as a linear combination, find coefficients \(c_1\) and \(c_2\) such that:
\[
\vec{b} = c_1 \vec{a_1} + c_2 \vec{a_2}
\]
*Input Section:*
- Enter the coefficients in the provided input boxes for \(c_1\) and \(c_2\), or type "DNE" if no solution exists.
\[
\vec{b} = \_\_ \, \vec{a_1} + \_\_ \, \vec{a_2}
\]
Click "Check Answer" after filling in the coefficients.
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