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Ipatiy [6.2K]
2 years ago
9

Let V be a vector space, and let v1, v2, v3 and v4 be linearly independent vectors in V . In parts (a) and (b) below, determine

whether each of the given sets of vectors is linearly independent or linearly dependent. Prove your answers using the definition.
u1 = v1 − 7v3, u2 = v1, u3 = v3, u4 = v3 + v4.
Mathematics
1 answer:
Blababa [14]2 years ago
8 0

Answer:

Step-by-step explanation:

u_3 = v_3 and  u_2 = v_1

u_1= v_1 -7 v_3

Replace the first line to the second line, you have u_1= u_2-7u_3

That shows \{u_1, u_2, u_3,u_4\}

is not linear independent.

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lidiya [134]
A terminating decimal means a number that repeats if that helps !
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3 years ago
Scientist A dissolved 1.0 kilogram of salt in 3.0 liters of water. Scientist B dissolved 2.0 pounds of salt into 7.0 pints of wa
solong [7]

The scientist that made a more concentrated salt solution is scientist A.

<h3>How to compute the value?</h3>

Since Scientist A dissolved 1.0 kilogram of salt in 3.0 liters of water. The concentration will be:

= 1/3 = 0.33

Scientist B dissolved 2.0 pounds of salt into 7.0 pints of water. The concentration will be:

= 2/7

= 0.285

Therefore, the scientist that made a more concentrated salt solution is scientist A.

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1 year ago
PLEASE ANSWER THIS AS SOON AS POSSIBLE
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3 0
3 years ago
If t = 18 and r = 12, find S. Round to the nearest tenth.
choli [55]

Answer: <em>S</em> ≈ 48.2°

Step-by-step explanation:

   We can use trigonometry functions to solve.

   Looking at angle <em>S</em>, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.

   \displaystyle cos(S) =  \frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18}

  \displaystyle cos^{-1} (cos(S)) =  (\frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18})cos^{-1}

  S = 48.189685...\\S  \;$\approx$\; 48.2^{\circ}

3 0
1 year ago
Read 2 more answers
Solve equation:<br><img src="https://tex.z-dn.net/?f=y%20%2B%20%20%5Cfrac%7B7%7D%7B8%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B8%7D%20"
Gala2k [10]

Answer: y = -1/2

Step-by-step explanation:

Subtract both sides by 7/8

y = 3/8 - 7/8

Then combine like terms

y = -4/8

Then simplify

y = -1/2

4 0
3 years ago
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