Matrix Multiplication Application
$begingroup$
I have a matrix representing the amount of different resources (columns) I would need to create (rows) different objects.
$begin{bmatrix}
1 & 1 & 0 & 0 & 0 \
1 & 1 & 1 & 1 & 0 \
0 & 0 & 2 & 0 & 3 \
end{bmatrix}$
My objective is to use matrix multiplication to find out how many resources it would take if we wanted to have i objects of row 1, j objects of row 2, and k objects of row 3.
I don't know an efficient way to go about this. A working solution I have is to split each of the rows and multiply them by scalars i, j, k, but I don't feel as though this is the correct solution.
Is there a way to get the same result by multiplying two matrices? Thank you.
linear-algebra matrices
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
$endgroup$
add a comment |
$begingroup$
I have a matrix representing the amount of different resources (columns) I would need to create (rows) different objects.
$begin{bmatrix}
1 & 1 & 0 & 0 & 0 \
1 & 1 & 1 & 1 & 0 \
0 & 0 & 2 & 0 & 3 \
end{bmatrix}$
My objective is to use matrix multiplication to find out how many resources it would take if we wanted to have i objects of row 1, j objects of row 2, and k objects of row 3.
I don't know an efficient way to go about this. A working solution I have is to split each of the rows and multiply them by scalars i, j, k, but I don't feel as though this is the correct solution.
Is there a way to get the same result by multiplying two matrices? Thank you.
linear-algebra matrices
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
$endgroup$
add a comment |
$begingroup$
I have a matrix representing the amount of different resources (columns) I would need to create (rows) different objects.
$begin{bmatrix}
1 & 1 & 0 & 0 & 0 \
1 & 1 & 1 & 1 & 0 \
0 & 0 & 2 & 0 & 3 \
end{bmatrix}$
My objective is to use matrix multiplication to find out how many resources it would take if we wanted to have i objects of row 1, j objects of row 2, and k objects of row 3.
I don't know an efficient way to go about this. A working solution I have is to split each of the rows and multiply them by scalars i, j, k, but I don't feel as though this is the correct solution.
Is there a way to get the same result by multiplying two matrices? Thank you.
linear-algebra matrices
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
$endgroup$
I have a matrix representing the amount of different resources (columns) I would need to create (rows) different objects.
$begin{bmatrix}
1 & 1 & 0 & 0 & 0 \
1 & 1 & 1 & 1 & 0 \
0 & 0 & 2 & 0 & 3 \
end{bmatrix}$
My objective is to use matrix multiplication to find out how many resources it would take if we wanted to have i objects of row 1, j objects of row 2, and k objects of row 3.
I don't know an efficient way to go about this. A working solution I have is to split each of the rows and multiply them by scalars i, j, k, but I don't feel as though this is the correct solution.
Is there a way to get the same result by multiplying two matrices? Thank you.
linear-algebra matrices
linear-algebra matrices
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
asked Jan 11 at 22:22
Jersey FonsecaJersey Fonseca
406
406
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
What you have described is matrix multiplication, and is the correct way to solve the problem.
Let $M$ stand for the $3 times 5$ resource matrix in the question. Then the
$1 times 5$ matrix
$$
[i,j,k]M
$$
tells you how many of each of the five kinds of resources you need to manufacture those objects.
The matrix product would look a little more traditional if you wrote the transpose $T$ of the resource consumption matrix instead, where each row corresponds to an ingredient and each column to a kind of object. Then the computation would be the $1 times 5$ matrix
$$
T
begin{bmatrix}
i \ j \ k
end{bmatrix}
$$
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
$endgroup$
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
What you have described is matrix multiplication, and is the correct way to solve the problem.
Let $M$ stand for the $3 times 5$ resource matrix in the question. Then the
$1 times 5$ matrix
$$
[i,j,k]M
$$
tells you how many of each of the five kinds of resources you need to manufacture those objects.
The matrix product would look a little more traditional if you wrote the transpose $T$ of the resource consumption matrix instead, where each row corresponds to an ingredient and each column to a kind of object. Then the computation would be the $1 times 5$ matrix
$$
T
begin{bmatrix}
i \ j \ k
end{bmatrix}
$$
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
$endgroup$
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
add a comment |
$begingroup$
What you have described is matrix multiplication, and is the correct way to solve the problem.
Let $M$ stand for the $3 times 5$ resource matrix in the question. Then the
$1 times 5$ matrix
$$
[i,j,k]M
$$
tells you how many of each of the five kinds of resources you need to manufacture those objects.
The matrix product would look a little more traditional if you wrote the transpose $T$ of the resource consumption matrix instead, where each row corresponds to an ingredient and each column to a kind of object. Then the computation would be the $1 times 5$ matrix
$$
T
begin{bmatrix}
i \ j \ k
end{bmatrix}
$$
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
$endgroup$
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
add a comment |
$begingroup$
What you have described is matrix multiplication, and is the correct way to solve the problem.
Let $M$ stand for the $3 times 5$ resource matrix in the question. Then the
$1 times 5$ matrix
$$
[i,j,k]M
$$
tells you how many of each of the five kinds of resources you need to manufacture those objects.
The matrix product would look a little more traditional if you wrote the transpose $T$ of the resource consumption matrix instead, where each row corresponds to an ingredient and each column to a kind of object. Then the computation would be the $1 times 5$ matrix
$$
T
begin{bmatrix}
i \ j \ k
end{bmatrix}
$$
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
$endgroup$
What you have described is matrix multiplication, and is the correct way to solve the problem.
Let $M$ stand for the $3 times 5$ resource matrix in the question. Then the
$1 times 5$ matrix
$$
[i,j,k]M
$$
tells you how many of each of the five kinds of resources you need to manufacture those objects.
The matrix product would look a little more traditional if you wrote the transpose $T$ of the resource consumption matrix instead, where each row corresponds to an ingredient and each column to a kind of object. Then the computation would be the $1 times 5$ matrix
$$
T
begin{bmatrix}
i \ j \ k
end{bmatrix}
$$
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
edited Jan 11 at 22:36
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
answered Jan 11 at 22:28
Ethan BolkerEthan Bolker
45k553120
45k553120
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
add a comment |
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
I'm sorry, can you explain the [i,j,k]A notation?
$endgroup$
– Jersey Fonseca
Jan 11 at 22:32
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
$begingroup$
Multiply the $1times 3$ matrix $[i,j,k]$ bythe $3 times 5$ matrix $A$.
$endgroup$
– user3482749
Jan 11 at 22:36
add a comment |
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