All categories

4 years ago

Prove that linearly independent set extend to basis

1 answer:

5 0

The completion is certainly not unique. Multiplying any of the new vectors by a nonzero constant will not affect the span or the linear independence, but will change the basis. To prove that you can extend any linearly independent set S to a basis, you proceed by an iterative argument. If S spans you are done. hope this helps :)

You might be interested in

Jada has 7/8 cup of cheese. Her cheese bread recipe calls for 1/6 of chees. How many times can she make her recipe with the chee

Grace [21]

5 times because with common denominaters(remeber:what you do the top you always do to the bottom or what you do the bottom you do to the top)7/8=21/24 1/6=4/24.21 divided by 4 equals 5.5 but you want a whole loaf of cheese bread not a half so you would round it to 5.

5 0

4 years ago

Read 2 more answers

What is the missing value?

madam [21]

the answer is 40

X 1 (+1) 2 (+1) 3 (+1) 4 (+1) 5

Y 4 (+9) 13 (+9) 22 (+9) 31 (+9) 40

3 0

2 years ago

Read 2 more answers

2/3 times 1/2 = IN SIMPLEST FORM I GIIVE BRAINY

Zinaida [17]

Answer:

1/3!

Step-by-step explanation:

Look us Cymath on g0ogle, its a calculator that shows its work!

8 0

3 years ago

two cars travel in opposite directions, starting from the same place at the same time. One travels at an average rate of 48 mile

asambeis [7]

So in 1 hour they will be 48+55=103 miles apart
how many hours will it be in 618
103 times x hours=618
divide both sides by 103
x=618/103
x=6

the answer is 6 hours

6 0

3 years ago

. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago