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Dominik [7]
2 years ago
8

Four friends had dinner togethere.

Mathematics
1 answer:
nataly862011 [7]2 years ago
8 0

Answer:

Your answer is $16.40

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A denotes an mn matrix. Determine whether the statement is true or false. Justify your answer. The row space of AT is the same a
ziro4ka [17]

Answer: true

Step-by-step explanation:

For an m*n matrix, the column space of A will be a space formed by the lineal combination of all the columns of A.

column space = a1*c1 + a2*c2 + ...

                       

where a1, a2, ... are scalars, and c1 is the vector of column 1.

Then we should write:

Column space = a1*(A₁₁, A₂₁, A₃₁, ...) + a2*(A₁₂, A₂₂, A₃₂, ...) + ...

Now, the transpose is defined as:

[At]₁₃ = A₃₁

Here i used the element with subindex 3 and 1, but is the same for every subindex.

Notice that if A is m*n, then [At] is n*m

Now, the row space of [At] will be, same as before.

Row space = b1*r1 + b2*r2 + ...

Where b1, b2, ... are scalars and the r's are the vector of each row.

                   = b1*( [At]₁₁ , [At]₁₂, [At]₁₃, ...) + b2*([At]₂₁, [At]₂₂, [At]₂₃, ...) + ...

Now we replace each term of the transpose by the associated element in the original matrix.

                   = b1*( A₁₁, A₂₁, A₃₁, ...) + b2*(A₂₁, A₂₂, ...) + ....

If we take:

b1 = a1, b2 = a2, b3 = a3, ...

We will have that the row space of [At] is the same as the column space of A.

4 0
2 years ago
You deposit money in an account that pays 5% interest compounded yearly. Find the balance after 5 years for the given initial am
mezya [45]
B I really believe you just got to read it carefully
5 0
3 years ago
Read 2 more answers
What do ducks short necks help them to do? pls help :/
Kruka [31]

Answer:

In some circumstances these displays may allow the female to observe the performance of males and to evaluate them as potential mates. To elicit displays from a group of males, a female Mallard may swim with her neck outstretched and her head just above the water

Step-by-step explanation:

hope this helps

8 0
2 years ago
Can anyone at least answer one questions pls and thank you
Burka [1]

Step-by-step explanation:

Number on is base

Two is diameter

Three is radius and diamater

Five is cubic

Four is pi and radius

( pls excuse my spelling )

5 0
3 years ago
Read 2 more answers
Kyra observed that 85% of the students at a library liked reading mystery stories. If 30 students at the library did not like re
boyakko [2]
First  calculate that numeric value. It cannot be done immediately without calculations.

if 85% of studends liked mystery that means that 100% - 85% = 15% didnt like.

Those 15% are 30 that were given in text. Now we can calculate this using proportion:

15%        30 students
85%         x students

we use cross multiplication:
15*x = 30*85
x = 30*85/15
x = 170

Answer is 170
8 0
3 years ago
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