How to multiply 2 1/4 •2/4

If vectors u,v and w ar linearly indepndnt, will u-v,v-w & u-w also be linearly indpnt? ...?

inna [77]

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.

6 0

3 years ago

Please Help!! :D<br><br> Find the value of y.

rjkz [21]

Answer:

$y=2\sqrt{2}$

Step-by-step explanation:

The Pythagorean theorem is a theorem that can be applied to the sides of a right triangle. Please note that a right angle refers to an angle with a measure of (90) degrees. A box around an angle shows that the angle is a right angle, or has a measure of (90) degrees. The Pythagorean theorem states the following,

$a^2+b^2=c^2$

Where (a) and (b) are the legs of the triangle, or the side adjacent to the right angle in the right triangle. (c) is the side opposite the right angle, or the hypotenuse of the triangle. One can apply this theorem to the smallest triangle in the diagram to find (y),

$a^2+b^2=c^2$

Substitute,

$(1)^2+(y)^2=(3)^2$

Simplify,

$(1)^2+(y)^2=(3)^2$

$1+y^2=9$

Inverse operations,

$1+y^2=9$

$y^2=8$

$y=\sqrt{8}$

Take a factor from out of the square root. Remember that a number times itself under the radical is equal to the number. This can be simply stated as the following: ( $\sqrt{a*a}=a$ ),

$y=\sqrt{8}$

$8=2*2*2$

$y=\sqrt{8}$

$y=\sqrt{2*2*2}$

$y=2\sqrt{2}$

4 0

3 years ago

You are working for the meteorological department in Hawaii. Your job is to track the amount of rainfall received on 50 sites ac

ki77a [65]

It is a observation study, because you are observing how much rainfall is in Hawaii at 50 sites.

8 0

3 years ago

Read 2 more answers

Samuel helps his brother paint walls during his summer vacation he charges $10 for the first room and $5 for each additional roo

Delicious77 [7]

10+5x=50
subtract ten from both sides
5x=40
divide five from both sides
x=8
samuel will need to paint 8 additional rooms

5 0

3 years ago

URGENT! PLEASE HELP.

Harrizon [31]

The distance BC from Tower 2 to the plane will be 14,065.5 ft and the height of the plane from the ground will be 5,720.9 ft.

<h3>What is a right-angle triangle?</h3>

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A plane is located at C on the diagram.

There are two towers located at A and B.

The distance between the towers is 7600 feet and angles of elevation are given.

Then in the right-angle triangle ΔADC, we have

$\rm \tan 16 = \dfrac{H}{7600 + X}\\\\\\H = 0.2867(7600 +X)\\\\\\H = 0.2756\ X + 2179.2649$ ...1