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Ipatiy [6.2K]
3 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]3 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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igomit [66]

Answer:

97.5

Step-by-step explanation:

Supplementary means the angles add up to 180°

So,

m∠A = 180 - m∠B

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8 0
3 years ago
Can you please help me with this problem?
Hoochie [10]
Here you have to find which each variable is, for this you start of picking one equation,

x + 2y + 6z = 4
-3x + 2y - 2 = -4
4x + 2z = 16

depending the equation you pick you multiply that by a certain number that will give you the opposite of one of the other equations,
-1(x + 2y + 6z = 4)
= -x -2y - 6z = -4

With this you add or subtract it with the equation that has the same number or variable, or both,
In this case it will be the equation,
-3x + 2y + 6z = 4
You can use this one or the third equation since both have a positive 2y which will cancel with -2y from the new equation,
-x - 2y - 6z = -4
-3x + 2y -z = -4

= -4x -7z = -8
Now you since you just eliminated the variable (y) you now have 2 variables, and the last equation has only 2 variables, meaning now you find the answer to those to equations,

-4x -7z = -8
4x + 2z = 16

= -5z = 8
Now leave the variable by itself,
z = 8/5
Now you found the variable (z), with this just substitute on one of the equations we used to find (z) so you can find (x), after that substitute those answered to on of the original equations so you can find (y)




6 0
3 years ago
What is the difference between the mean and the median of the following distribution?
natulia [17]
The definition of mean, is to add up all the numbers and divide it by how many numbers there are. So, in this case the mean would be 1+1+1+2+2+2+2+3+3+4+4+4+4+5+5+6+7+7+8+8+9 = 86. You would then take 86 and divide that by 21, and you would get 4.0
The definition of median states to find the middle of the numbers. So the median would be 4. 
So you would just take 4 - 4 = 0. 

0 would be correct.
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3 years ago
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3 years ago
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sesenic [268]

Answer:

quotient

Step-by-step explanation:

yup it just is

5 0
2 years ago
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