Question

4. Let $v_1 = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $v_2 = \begin{bmatrix} -3 \\ 4 \end{bmatrix}$. (a) Describe the span of $v_1$ and $v_2$ in $\mathbb{R}^2$. What geometric shape does it represent? (b) Determine if the vector $b = \begin{bmatrix} 4 \\ 1 \end{bmatrix}$ is in the span of $v_1$ and $v_2$. (c) If b is in the span, find the linear combination of $v_1$ and $v_2$ that equals b.

          4. Let $v_1 = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $v_2 = \begin{bmatrix} -3 \\ 4 \end{bmatrix}$.
(a) Describe the span of $v_1$ and $v_2$ in $\mathbb{R}^2$. What geometric shape does it represent?
(b) Determine if the vector $b = \begin{bmatrix} 4 \\ 1 \end{bmatrix}$ is in the span of $v_1$ and $v_2$.
(c) If b is in the span, find the linear combination of $v_1$ and $v_2$ that equals b.

4. Let v1 =
< b m a t r i x > and v2 =
< b m a t r i x >.
(a) Describe the span of v1 and v2 in ℝ^2. What geometric shape does it represent?
(b) Determine if the vector b =
< b m a t r i x > is in the span of v1 and v2.
(c) If b is in the span, find the linear combination of v1 and v2 that equals b.

Added by Lauren W.

Elementary and Intermediate Algebra

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

Instant Answer

Solved by Expert Supreeta N

03/21/2023

Step 1

That is, the span is the set of all vectors of the form $c_1v_1 + c_2v_2$, where $c_1$ and $c_2$ are scalars. Show more…

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4. Let $v_1 = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $v_2 = \begin{bmatrix} -3 \\ 4 \end{bmatrix}$. (a) Describe the span of $v_1$ and $v_2$ in $\mathbb{R}^2$. What geometric shape does it represent? (b) Determine if the vector $b = \begin{bmatrix} 4 \\ 1 \end{bmatrix}$ is in the span of $v_1$ and $v_2$. (c) If b is in the span, find the linear combination of $v_1$ and $v_2$ that equals b.