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

Studdy Solution

STEP 1

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

STEP 2

First, let's compute $\mathbf{u}+\mathbf{v}$ . To do this, we add the corresponding elements in each vector.
$\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} u1 + v1 \\ u2 + v2\end{array}\right]$

STEP 3

Now, plug in the given values for $u1, u2, v1, v2$ 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.
$\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} -8 \\ 10\end{array}\right]$

STEP 5

Next, let's compute $\mathbf{u}-3\mathbf{v}$ . To do this, we first multiply the vector $\mathbf{v}$ by3 and then subtract the result 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 $u1, u2, v1, v2$ 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 result of the operation.
$\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} 12 \\ -6\end{array}\right]$ So, $\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} - \\ 10\end{array}\right]$ and $\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} 12 \\ -6\end{array}\right]$

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

Studdy Solution

STEP 1

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

STEP 2

First, let's compute $\mathbf{u}+\mathbf{v}$ . To do this, we add the corresponding elements in each vector.
$\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} u1 + v1 \\ u2 + v2\end{array}\right]$

STEP 3

Now, plug in the given values for $u1, u2, v1, v2$ 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.
$\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} -8 \\ 10\end{array}\right]$

STEP 5

Next, let's compute $\mathbf{u}-3\mathbf{v}$ . To do this, we first multiply the vector $\mathbf{v}$ by3 and then subtract the result 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 $u1, u2, v1, v2$ 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 result of the operation.
$\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} 12 \\ -6\end{array}\right]$ So, $\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} - \\ 10\end{array}\right]$ and $\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} 12 \\ -6\end{array}\right]$

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

Studdy Solution

STEP 1

Assumptions1. The vectors are u=[−36]\mathbf{u}=\left[\begin{array}{r} -3 \\ 6\end{array}\right]u=[−36​] and v=[−54]\mathbf{v}=\left[\begin{array}{r} -5 \\ 4\end{array}\right]v=[−54​] . We are asked to compute u+v\mathbf{u}+\mathbf{v}u+v and u−3v\mathbf{u}-3\mathbf{v}u−3v

STEP 2

First, let's compute u+v\mathbf{u}+\mathbf{v}u+v. To do this, we add the corresponding elements in each vector.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 u1,u2,v1,v2u1, u2, v1, v2u1,u2,v1,v2 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+v=[−810]\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} -8 \\ 10\end{array}\right]u+v=[−810​]

STEP 5

Next, let's compute u−3v\mathbf{u}-3\mathbf{v}u−3v. To do this, we first multiply the vector v\mathbf{v}v by3 and then subtract the result from u\mathbf{u}u.u−3v=[u1−3v1u2−3v2]\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} u1 -3v1 \\ u2 -3v2\end{array}\right]u−3v=[u1−3v1u2−3v2​]

STEP 6

Now, plug in the given values for u1,u2,v1,v2u1, u2, v1, v2u1,u2,v1,v2 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

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

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

First, let's compute $\mathbf{u}+\mathbf{v}$ . To do this, we add the corresponding elements in each vector.
$\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} u1 + v1 \\ u2 + v2\end{array}\right]$

Now, plug in the given values for $u1, u2, v1, v2$ 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.
$\mathbf{u}+\mathbf{v} = \left[\begin{array}{r} -8 \\ 10\end{array}\right]$

Next, let's compute $\mathbf{u}-3\mathbf{v}$ . To do this, we first multiply the vector $\mathbf{v}$ by3 and then subtract the result from $\mathbf{u}$ .
$\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} u1 -3v1 \\ u2 -3v2\end{array}\right]$

Now, plug in the given values for $u1, u2, v1, v2$ to calculate $\mathbf{u}-3\mathbf{v}$ .
$\mathbf{u}-3\mathbf{v} = \left[\begin{array}{r} -3 -3(-5) \\ 6 -3(4) \end{array}\right]$