Question

1. Write the vector $\begin{bmatrix} 6\\11\\6 \end{bmatrix}$ as a linear combination of the vectors $\vec{u} = \begin{bmatrix} 2\\1\\4 \end{bmatrix}$, $\vec{v} = \begin{bmatrix} 1\\-1\\3 \end{bmatrix}$, and $\vec{w} = \begin{bmatrix} 3\\2\\5 \end{bmatrix}$.

          1. Write the vector $\begin{bmatrix} 6\\11\\6 \end{bmatrix}$ as a linear combination of the vectors $\vec{u} = \begin{bmatrix} 2\\1\\4 \end{bmatrix}$, $\vec{v} = \begin{bmatrix} 1\\-1\\3 \end{bmatrix}$, and $\vec{w} = \begin{bmatrix} 3\\2\\5 \end{bmatrix}$.

1. Write the vector < b m a t r i x > as a linear combination of the vectors u⃗ =
< b m a t r i x >, v⃗ =
< b m a t r i x >, and w⃗ =
< b m a t r i x >.

Added by Heather Q.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Christopher Stanley

03/07/2022

Step 1

Step 1: We want to find scalars $a$, $b$, and $c$ such that $a\vec{u} + b\vec{v} + c\vec{w} = \begin{bmatrix} 6 \\ 11 \\ 6 \end{bmatrix}$. Show more…

Show all steps

Thanks for your feedback!

1. Write the vector $\begin{bmatrix} 6 \\ 11 \\ 6 \end{bmatrix}$ as a linear combination of the vectors $\vec{u} = \begin{bmatrix} 2 \\ 1 \\ 4 \end{bmatrix}$, $\vec{v} = \begin{bmatrix} 1 \\ -1 \\ 3 \end{bmatrix}$, and $\vec{w} = \begin{bmatrix} 3 \\ 2 \\ 5 \end{bmatrix}$.