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Anon25 [30]
2 years ago
9

So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,

....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then L1(v)=L2(v) for any v in V. ...?
Mathematics
1 answer:
noname [10]2 years ago
6 0
<span>if v belongs to V, then we can find scalars a1,a2,...,an, such that v=a1*v1+a2*v2+...+an*vn, L1(v)=L1(a1*v1+a2*v2+...+an*vn) =a1*L1(v1)+a2*L1(v2)+...+an*L1(vn) =a1*L2(v1)+a2*L2(v2)+...+an*L2(vn) =L2(a1*v1+a2*v2+...+an*vn) =L2(v)</span>
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Anthony Tedesco sold his used mountain bike and accessories for $140. If he received 4 times as much money for the bike as he di
Zepler [3.9K]

Answer:

Step-by-step explanation:

Accessories: x

Bike: 4x

Total1: 5x

Total2: 140 dollars.

x + 4x = 140 dollars

5x = 140

x = 28

Accessories: 28

Bike: 112

3 0
2 years ago
Read 2 more answers
Rena spent 6 days reading her book completing the same fraction of the book each day if she had a total of 8/9 of her book after
Artyom0805 [142]

Answer:

The fraction of the book that Rena read every day is \frac{4}{27}

Step-by-step explanation:

Rena spent 6 days reading her book completing the same fraction of the book every day and you want to know the fraction of the book she read each day. Knowing that Rena had a total of 8/9 of her book read after 6 days, then you simply divide the total amount of the book read during those days by 6, the number of days:  

\frac{8}{9}÷6

To divide a fraction by a whole number, you must convert the whole number into a fraction, finding the reciprocal of that fraction, and multiply it by the first fraction. That is, you must find the reciprocal of the number that is after the division symbol; and then you multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol). Remember that to find the reciprocal of a number, you simply have to change the numerator and denominator of the number.

Since 6 can be considered to be a fraction equal to \frac{6}{1}, by inverting the number, then you get \frac{1}{6}

Then:

\frac{8}{9}÷6= \frac{8}{9} *\frac{1}{6}

Now you multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final solution.

\frac{8}{9}÷6= \frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}

Finally, simplifying the fraction:

\frac{8}{9}÷6= \frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}=\frac{4}{27}

So:

\frac{8}{9}÷6= \frac{4}{27}

<u><em>The fraction of the book that Rena read every day is </em></u>\frac{4}{27}<u><em></em></u>

3 0
3 years ago
The area of a square garden is shown. How long is each side of the garden? A=121ft^2
polet [3.4K]
The answer is 30.25ft
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2 years ago
Carmen works at a pet store.To feed 8 cats, she empties four 6-ounce cans of cat food into a large bowl.Carmen divides the food
balu736 [363]

Answer:

0.75 oz

Step-by-step explanation:

8 cats divided by 6-oz cans=0.75 oz each

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3 years ago
An analyst in Bank of America, Santa Clara University Branch, believes that on Mondays customers arrive at the bank with rate 50
Aleksandr-060686 [28]

Answer:

0.0821

Step-by-step explanation:

If the arrival rate is 50 customers per hour (60 minutes), then the expected number of customers in 3 minutes is:

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Assuming a Poisson distribution with 2.5 customers per 3 minutes, the probability that zero customers arrive for 3 minutes is:

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The probability that the bank stays empty for three minutes is 0.0821.

6 0
3 years ago
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