No they won’t be.Consider the linear combination (1)(u – v) + (1) (v – w) + (-1)(u – w).This will add to 0. But the coefficients aren’t all 0.Therefore, those vectors aren’t linearly independent.
You can try an example of this with (1, 0, 0), (0, 1, 0), and (0, 0, 1), the usual basis vectors of R3.
That method relied on spotting the solution immediately.If you couldn’t see that, then there’s another approach to the problem.
We know that u, v, w are linearly independent vectors.So if au + bv + cw = 0, then a, b, and c are all 0 by definition.
Suppose we wanted to ask whether u – v, v – w, and u – w are linearly independent.Then we’d like to see if there are non-zero coefficients in the linear combinationd(u – v) + e(v – w) + f(u – w) = 0, where d, e, and f are scalars.
Distributing, we get du – dv + ev – ew + fu – fw = 0.Then regrouping by vector: (d + f)u + (-d +e)v + (-e – f)w = 0.
But now we have a linear combo of u, v, and w vectors.Therefore, all the coefficients must be 0.So d + f = 0, -d + e = 0, and –e – f = 0. It turns out that there’s a free variable in this solution.Say you let d be the free variable.Then we see f = -d and e = d.
Then any solution of the form (d, e, f) = (d, d, -d) will make (d + f)u + (-d +e)v + (-e – f)w = 0 a true statement.
Let d = 1 and you get our original solution. You can let d = 2, 3, or anything if you want.
Answer:

Step-by-step explanation:

Subtract 2 from both sides

mutliply both sides by -4, flip the inequality

Add 2x on both sideds

Subtract 8 from both sides

Divide both sides by 6

Answer:
Step-by-step explanation:
Cicero and Themistocles run for the same political office. Cicero received w votes in the election, and
Themistocles received v votes.
Which of the following expressions always represents how many more votes the winner received than the
loser?
The answer is B trust me
Answer:
B. Jazz and opra
Step-by-step explanation:
40 percent of 55 is 22. Find whatever is equal to 22
Answer:
Option C: 47 tickets
Step-by-step explanation:
Given that:
Tickets given to employees = 1 part
Tickets given to listeners = 2 parts
This means 141 tickets are totally divided into 3 parts so:
1 part = 141/3
1 part = 47
So now,
Tickets given to employees = 1 part = 47 tickets
Tickets given to listeners = 2 parts = 47 *2 tickets = 94 tickets
I hope it will help you!