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:12x2 + 3x + 6 + (-7)x2 - 4x - 2 = 0
12•x•2 + 3•x + 6 + (-7)•x•2 - 4•x - 2 = 0
9x = -4
x = -4/
9
≈ -0.444444
Answer:
A. h = 4
B. g = 15
C. b = -6
D. b = 15
Step-by-step explanation:
A. 9h + 8 - 12 = -40
9h - 4 = -40
+ 4 + 4
9h = -36
h = -4
B. 9 + 6g + 1 = 100
10 + 6g = 100
- 10 - 10
6g = 90
g = 15
C. -45 = 28 - 13 + 10b
-45 = 15 + 10b
- 15 - 15
-60 = 10b
b = -6
D. 37 = 11 +3b - 19
37 = 3b - 8
+ 8 + 8
45 = 3b
15 = b
I think it’s 2. You can see this because if you count the squares in the smaller triangle it is 3 along. You would then need to double the amount of squares on all sides. This makes the larger triangle now 6 squares along. 6/3 is 2 making the scale factor 2. (This is only if I have read the question correctly and we are calculating small to big. If I have read it wrong and it is big to small it would be 1/2)
Answer: $11.60
Explanation: First, you want to do 15.1 - 9.3 to find what half of his weekly allowance is, and that would be 5.8, AKA $5.80. Next, you want to multiply that number by 2, which would be 5.8(2) to get 11.6, or your final answer, $11.60.
