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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.

You might be interested in
<img src="https://tex.z-dn.net/?f=%284%20%2B%206i%29%20%7B%7D%5E%7B2%7D%20" id="TexFormula1" title="(4 + 6i) {}^{2} " alt="(4 +
34kurt

Answer:

36i^{2}+48i+16

Step-by-step explanation:

(4+6i)^{2} is essentially (4+6i)(4+6i) (you are squaring (4+6i), so multiplying it by itself), so to simplify, you would need to distribute.

A good way to go about this is using the F.O.I.L. method, multiplying the First numbers in the parentheses, then the Outers, then Inners, and finally, Lasts.

(4+6i)(4+6i) >> (4+6i)(4+6i) >> (4+6i)(4+6i) >> (4+6i)(4+6i)

((4*4)+(4*6i)+(6i*4)(6i*6i))

After doing so, you would end up with 16+24i+24i+36i^{2}, and after combining like terms, 16+48i+36i^{2}.

To write the expression in standard form, though, just order the terms from highest to lowest power!

5 0
3 years ago
Mary had a back surgery and was given a prescription with instructions to take 4 tablets twice a day for pain. How many tablets
astraxan [27]

Answer:

14 tablets

Step-by-step explanation:

In one day 2 tablets and in 7 day

7×2=14 tablets

4 0
3 years ago
Jacksons family drove 496 in 8 hour what is the unit rate
stich3 [128]
62unit/hour is the answer
distance/time
5 0
3 years ago
The sum of twice a number and five is greater than three times the number minus three.
AnnZ [28]

Answer:

x<8

Step-by-step explanation:

2x+5>3x-3

2x+8>3x

8>x

5 0
2 years ago
Read 2 more answers
How do I do it? Acellus exam help
Mnenie [13.5K]

Answer:

30

Step-by-step explanation:

triangle ABC is proportional to triangle BCD so

hypothenuse of ABC/ ajdacent of ABC = hypotrnus BCD/ ajdacent of BCD

in short

AC/BC = BC/DC

10/x = x/3

10 . 3 = x²

x² = 30

x = √30

so the question mark is 30

4 0
2 years ago
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