QuestionFind $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

Studdy Solution

STEP 1

Assumptions1. The vectors $\mathbf{u}$ and $\mathbf{v}$ are given as $\mathbf{u}=\left[\begin{array}{r}-3 \\6\end{array}\right]$ and $\mathbf{v}=\left[\begin{array}{r}-5 \\4\end{array}\right]$ respectively. . We are asked to compute $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3\mathbf{v}$ .

STEP 2

First, let's compute $\mathbf{u}+\mathbf{v}$ . The sum of two vectors is obtained by adding their corresponding components.
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}u1+v1 \\u2+v2\end{array}\right]$

STEP 3

Now, plug in the given values for the components of $\mathbf{u}$ and $\mathbf{v}$ to calculate $\mathbf{u}+\mathbf{v}$ .
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-3+(-5) \\6+\end{array}\right]$

STEP 4

Calculate the sum of the vectors $\mathbf{u}$ and $\mathbf{v}$ .
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-8 \\10\end{array}\right]$

STEP 5

Next, let's compute $\mathbf{u}-3\mathbf{v}$ . The difference of two vectors is obtained by subtracting their corresponding components. Here, we are subtracting3 times the vector $\mathbf{v}$ from $\mathbf{u}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}u1-3v1 \\u2-3v2\end{array}\right]$

STEP 6

Now, plug in the given values for the components of $\mathbf{u}$ and $\mathbf{v}$ to calculate $\mathbf{u}-3\mathbf{v}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}-3-3(-5) \\6-3(4)\end{array}\right]$

STEP 7

Calculate the difference of the vectors $\mathbf{u}$ and $3\mathbf{v}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}12 \\-6\end{array}\right]$ So, $\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}- \\10\end{array}\right]$ and $\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}12 \\-6\end{array}\right]$ .

Was this helpful?

QuestionFind $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

Studdy Solution

STEP 1

Assumptions1. The vectors $\mathbf{u}$ and $\mathbf{v}$ are given as $\mathbf{u}=\left[\begin{array}{r}-3 \\6\end{array}\right]$ and $\mathbf{v}=\left[\begin{array}{r}-5 \\4\end{array}\right]$ respectively. . We are asked to compute $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3\mathbf{v}$ .

STEP 2

First, let's compute $\mathbf{u}+\mathbf{v}$ . The sum of two vectors is obtained by adding their corresponding components.
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}u1+v1 \\u2+v2\end{array}\right]$

STEP 3

Now, plug in the given values for the components of $\mathbf{u}$ and $\mathbf{v}$ to calculate $\mathbf{u}+\mathbf{v}$ .
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-3+(-5) \\6+\end{array}\right]$

STEP 4

Calculate the sum of the vectors $\mathbf{u}$ and $\mathbf{v}$ .
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-8 \\10\end{array}\right]$

STEP 5

Next, let's compute $\mathbf{u}-3\mathbf{v}$ . The difference of two vectors is obtained by subtracting their corresponding components. Here, we are subtracting3 times the vector $\mathbf{v}$ from $\mathbf{u}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}u1-3v1 \\u2-3v2\end{array}\right]$

STEP 6

Now, plug in the given values for the components of $\mathbf{u}$ and $\mathbf{v}$ to calculate $\mathbf{u}-3\mathbf{v}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}-3-3(-5) \\6-3(4)\end{array}\right]$

STEP 7

Calculate the difference of the vectors $\mathbf{u}$ and $3\mathbf{v}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}12 \\-6\end{array}\right]$ So, $\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}- \\10\end{array}\right]$ and $\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}12 \\-6\end{array}\right]$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind u+v\mathbf{u}+\mathbf{v}u+v and u−3v\mathbf{u}-3 \mathbf{v}u−3v for u=[−36],v=[−54]u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}u=[−36​],v=[−54​].

Studdy Solution

STEP 1

STEP 2

First, let's compute u+v\mathbf{u}+\mathbf{v}u+v. The sum of two vectors is obtained by adding their corresponding components.u+v=[u1+v1u2+v2]\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}u1+v1 \\u2+v2\end{array}\right]u+v=[u1+v1u2+v2​]

STEP 3

Now, plug in the given values for the components of u\mathbf{u}u and v\mathbf{v}v to calculate u+v\mathbf{u}+\mathbf{v}u+v.u+v=[−3+(−5)6+]\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-3+(-5) \\6+\end{array}\right]u+v=[−3+(−5)6+​]

STEP 4

Calculate the sum of the vectors u\mathbf{u}u and v\mathbf{v}v.u+v=[−810]\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-8 \\10\end{array}\right]u+v=[−810​]

STEP 5

STEP 6

Now, plug in the given values for the components of u\mathbf{u}u and v\mathbf{v}v to calculate u−3v\mathbf{u}-3\mathbf{v}u−3v.u−3v=[−3−3(−5)6−3(4)]\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}-3-3(-5) \\6-3(4)\end{array}\right]u−3v=[−3−3(−5)6−3(4)​]

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

First, let's compute $\mathbf{u}+\mathbf{v}$ . The sum of two vectors is obtained by adding their corresponding components.
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}u1+v1 \\u2+v2\end{array}\right]$

Now, plug in the given values for the components of $\mathbf{u}$ and $\mathbf{v}$ to calculate $\mathbf{u}+\mathbf{v}$ .
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-3+(-5) \\6+\end{array}\right]$

Calculate the sum of the vectors $\mathbf{u}$ and $\mathbf{v}$ .
$\mathbf{u}+\mathbf{v}=\left[\begin{array}{r}-8 \\10\end{array}\right]$

Now, plug in the given values for the components of $\mathbf{u}$ and $\mathbf{v}$ to calculate $\mathbf{u}-3\mathbf{v}$ .
$\mathbf{u}-3\mathbf{v}=\left[\begin{array}{r}-3-3(-5) \\6-3(4)\end{array}\right]$