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3 years ago

Let W be the subspace of R5 spanned by the vectors w1, w2, w3, w4, w5, where

1 answer:

7 0

To find W⊥, you can use the Gram-Schmidt process using the usual inner-product and the given 5 independent set of vectors.

Define projection of v on u as 
p(u,v)=u*(u.v)/(u.u) 
we need to proceed and determine u1...u5 as: 
u1=w1 
u2=w2-p(u1,w2) 
u3=w3-p(u1,w3)-p(u2,w3) 
u4=w4-p(u1,w4)-p(u2,w4)-p(u3,w4) 
u5=w5-p(u4,w5)-p(u2,w5)-p(u3,w5)-p(u4,w5) 

so that u1...u5 will be the new basis of an orthogonal set of inner space. 

However, the given set of vectors is not independent, since 
w1+w2=w3, 
therefore an orthogonal basis cannot be found.

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(05.02 LC)

Arte-miy333 [17]

Your Answer: A.) (2 , 5) I also provided the steps.

Hope this helps y'all :)

7 0

3 years ago

Read 2 more answers

Lesson 7.4 Identify Parts of Expressions Please help!!!!!!!

bulgar [2K]

1.)
The term (2+8) is the amount of fabric Ali bought. You know this because in the problem, it says that she buys “2 white pieces and 8 blue pieces”

2.)
The terms of the equation are
k and 2f

These are the terms because they are separated by the addition sign

3.) $36
You would first find rate per sand which. To find this, you would do:
9/2
This will give you
4.5. Now, you multiply that by 4. That gives you 36.

4.) The skateboard costs 150

How?
30 is 20% of the price. 20x5=100. So, to find the total amount, you would multiply 30 by 150.

5.) About 50 miles an hour.
You always put distance over time. If you do:
400/8
You get the average rate of 50

6.) 5n

How?
Well, there are five cents in every nickel. So, to find out how many pennies, you would multiply the amount of nickels by 5.

Have a good night :)

5 0

3 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

3 years ago

the volume of a cone is 120 cubic centimeters. the height of the cone is 4.5 centimeters. determine the radius of a cone

kolbaska11 [484]

<h3> given:</h3>

$v = 120 \: {cm}^{3}$

$h = 4.5 \: cm$

the radius of the cone.

<h3>solution:</h3>

$r = \sqrt{3 \frac{v}{\pi \: h} }$

$r = \sqrt{3 \times \frac{120}{\pi \times 4.5} }$

$r = 5.04627 \: cm$

$r = 5.05 \: cm$

hence, the radius of the given cone is 5.05 centimeters.

7 0

2 years ago

Question 7: Which of the following statements is true?

yawa3891 [41]

Problem 7)

The answer is choice B. Only graph 2 contains an Euler circuit.

-----------------

To have a Euler circuit, each vertex must have an even number of paths connecting to it. This does not happen with graph 1 since vertex A and vertex D have an odd number of vertices (3 each). The odd vertex count makes it impossible to travel back to the starting point, while making sure to only use each edge one time only.

With graph 2, each vertex has exactly two edges attached to it. So an Euler circuit is possible here.

================================================

Problem 8)

The answer is choice B) 5

-----------------

Work Shown:

abc base 2 = (a*2^2 + b*2^1 + c*2^0) base 10

101 base 2 = (1*2^2 + 0*2^1 + 1*2^0) base 10

101 base 2 = (1*4 + 0*2 + 1*1) base 10

101 base 2 = (4 + 0 + 1) base 10

101 base 2 = 5 base 10

4 0

2 years ago