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cluponka [151]
3 years ago
5

Can you help me solve this? Thanks!

Mathematics
1 answer:
Vika [28.1K]3 years ago
5 0

Answer:

135/2

Step-by-step explanation:

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Determine whether the set of vectors <img src="https://tex.z-dn.net/?f=%20v_%7B1%3D%283%2C2%2C1%29%2C%20v_%7B2%7D%20%3D%28-1%2C-
Korolek [52]
Since each vector is a member of \mathbb R^3, the vectors will span \mathbb R^3 if they form a basis for \mathbb R^3, which requires that they be linearly independent of one another.

To show this, you have to establish that the only linear combination of the three vectors c_1\mathbf v_1+c_2\mathbf v_2+c_3\mathbf v_3 that gives the zero vector \mathbf0 occurs for scalars c_1=c_2=c_3=0.

c_1\begin{bmatrix}3\\2\\1\end{bmatrix}+c_2\begin{bmatrix}-1\\-2\\-4\end{bmatrix}+c_3\begin{bmatrix}1\\1\\-1\end{bmatrix}=(0,0,0)\iff\begin{bmatrix}3&-1&1\\2&-2&1\\1&-4&-1\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix}=\begin{bmatrix}0\\0\\0\end{bmatrix}

Solving this, you'll find that c_1=c_2=c_3=0, so the vectors are indeed linearly independent, thus forming a basis for \mathbb R^3 and therefore they must span \mathbb R^3.
4 0
3 years ago
A farmer delivers 24 cartons of milk to a grocery store in a plastic crate. The dimensions of the crate measure 12.1 in. by 12.1
Over [174]

Answer:

i dunoo

Step-by-step explanation:

3 0
3 years ago
5 over -3 ÷ 7 over 8
GREYUIT [131]

Answer:

-0.02976190476 or -17.1428571429

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4 0
3 years ago
Read 2 more answers
A regular hexagon rotates counterclockwise around its center. It turns through angles greater than 0° and less or equal to 360°.
Sonja [21]

there are 6 sides to a hexagon

360/6 = 60 degrees

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6 0
4 years ago
A rectangular city lot has an area of 1000 square meters. If the length of the lot is 10 meters more than twice its width, find
loris [4]

Answer: l=50 m, w=20 m

Step-by-step explanation:

Given

A rectangular city has an area of 1000\ m^2

Also, length is 10 m more than twice its width

suppose width is w

So, length is given by

\Rightarrow l=10+2w

The area is given by

\Rightarrow A=l\times w\\\Rightarrow 1000=(10+2w)\times w\\\Rightarrow 2w^2+10w-1000=0\\\Rightarrow w^2+5w-500=0\\\Rightarrow w^2+25w-20w-500=0\\\Rightarrow (w+25)(w-20)=0\\\therefore w=20\ m\\l=10+2w=10+2\times 20=50\ m

8 0
3 years ago
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