Consider the vectors u₁ = and the vector w = 3 H Q- W U2 = []} Uz = U2+ →→→→ →→→→ If u IS in the span of u1, U2, u3, U4, write was a linear combination of u1, U2, u3, U4, using as few nonzero coefficients as possible. -2 U4 = " →→→→ If w IS NOT in the span of u₁, u, u3, U4, write DNE in each of the answer boxes. ui+ Uz + 3 Us
Consider the vectors u₁ = and the vector w = 3 H Q- W U2 = []} Uz = U2+ →→→→ →→→→ If u IS in the span of u1, U2, u3, U4, write was a linear combination of u1, U2, u3, U4, using as few nonzero coefficients as possible. -2 U4 = " →→→→ If w IS NOT in the span of u₁, u, u3, U4, write DNE in each of the answer boxes. ui+ Uz + 3 Us
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
![Consider the vectors
\[
\vec{u_1} = \begin{bmatrix} 1 \\ 1 \\ -2 \end{bmatrix}, \quad \vec{u_2} = \begin{bmatrix} 1 \\ 2 \\ -2 \end{bmatrix}, \quad \vec{u_3} = \begin{bmatrix} 1 \\ -2 \\ -2 \end{bmatrix}, \quad \vec{u_4} = \begin{bmatrix} 1 \\ 3 \\ -2 \end{bmatrix}
\]
and the vector
\[
\vec{w} = \begin{bmatrix} 3 \\ -3 \\ -6 \end{bmatrix}.
\]
If \(\vec{w}\) **IS** in the span of \(\vec{u_1}, \vec{u_2}, \vec{u_3}, \vec{u_4}\), write \(\vec{w}\) as a linear combination of \(\vec{u_1}, \vec{u_2}, \vec{u_3}, \vec{u_4}\), **using as few nonzero coefficients as possible**.
If \(\vec{w}\) **IS NOT** in the span of \(\vec{u_1}, \vec{u_2}, \vec{u_3}, \vec{u_4}\), write DNE in each of the answer boxes.
\[
\vec{w} = \boxed{\phantom{0}} \vec{u_1} + \boxed{\phantom{0}} \vec{u_2} + \boxed{\phantom{0}} \vec{u_3} + \boxed{\phantom{0}} \vec{u_4}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c49f70f-02c0-4076-b0a5-564b9a6f1d8d%2F8ce6248a-4cae-4314-b6bb-aa64611622bf%2Fkcnww8k_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the vectors
\[
\vec{u_1} = \begin{bmatrix} 1 \\ 1 \\ -2 \end{bmatrix}, \quad \vec{u_2} = \begin{bmatrix} 1 \\ 2 \\ -2 \end{bmatrix}, \quad \vec{u_3} = \begin{bmatrix} 1 \\ -2 \\ -2 \end{bmatrix}, \quad \vec{u_4} = \begin{bmatrix} 1 \\ 3 \\ -2 \end{bmatrix}
\]
and the vector
\[
\vec{w} = \begin{bmatrix} 3 \\ -3 \\ -6 \end{bmatrix}.
\]
If \(\vec{w}\) **IS** in the span of \(\vec{u_1}, \vec{u_2}, \vec{u_3}, \vec{u_4}\), write \(\vec{w}\) as a linear combination of \(\vec{u_1}, \vec{u_2}, \vec{u_3}, \vec{u_4}\), **using as few nonzero coefficients as possible**.
If \(\vec{w}\) **IS NOT** in the span of \(\vec{u_1}, \vec{u_2}, \vec{u_3}, \vec{u_4}\), write DNE in each of the answer boxes.
\[
\vec{w} = \boxed{\phantom{0}} \vec{u_1} + \boxed{\phantom{0}} \vec{u_2} + \boxed{\phantom{0}} \vec{u_3} + \boxed{\phantom{0}} \vec{u_4}
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
