Section 4.6 Model and solve systems of linear equations using matrix inverse methods Solve the following application using matrix inverse methods. An international mining company has two mines in Voisey's Bay and Hawk Ridge. The composition of the ore from each field is given in the table. Mine Voisey's Bay Hawk Ridge Nickel (%) 2 3 Nickel Copper How many tons of ore from each mine should be used to obtain each order of nickel and copper in the table below: Copper (%) 4 2 Order 1 6 tons 8 tons Order 2 8 tons 4 tons
Section 4.6 Model and solve systems of linear equations using matrix inverse methods Solve the following application using matrix inverse methods. An international mining company has two mines in Voisey's Bay and Hawk Ridge. The composition of the ore from each field is given in the table. Mine Voisey's Bay Hawk Ridge Nickel (%) 2 3 Nickel Copper How many tons of ore from each mine should be used to obtain each order of nickel and copper in the table below: Copper (%) 4 2 Order 1 6 tons 8 tons Order 2 8 tons 4 tons
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![# MATH 1324 Written Assignment 2
## Section 4.6: Model and Solve Systems of Linear Equations Using Matrix Inverse Methods
### Problem Statement
Solve the following application using matrix inverse methods.
An international mining company has two mines in Voisey's Bay and Hawk Ridge. The composition of the ore from each field is given in the table:
| Mine | Nickel (%) | Copper (%) |
|---------------|------------|------------|
| Voisey's Bay | 2 | 4 |
| Hawk Ridge | 3 | 2 |
How many tons of ore from each mine should be used to obtain each order of nickel and copper in the table below:
| Metal | Order 1 | Order 2 |
|----------|---------|---------|
| Nickel | 6 tons | 8 tons |
| Copper | 8 tons | 8 tons |
### Solution
#### Step 1: Set Up the System of Equations
We can set up the linear system based on the given percentage compositions and required amounts:
For Nickel (N):
\[ 2x_1 + 3x_2 = \text{Nickel amount} \]
For Copper (C):
\[ 4x_1 + 2x_2 = \text{Copper amount} \]
Here,
- \( x_1 \) = amount of ore from Voisey's Bay
- \( x_2 \) = amount of ore from Hawk Ridge
#### Step 2: Turn the System into Matrix Form
Using the given orders,
- For order 1:
\[
\begin{bmatrix}
2 & 3 \\
4 & 2
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}
=
\begin{bmatrix}
6 \\
8
\end{bmatrix}
\]
- For order 2:
\[
\begin{bmatrix}
2 & 3 \\
4 & 2
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}
=
\begin{bmatrix}
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb29078dc-c094-4f2a-a943-f6ab9e28bb44%2F49f2ce25-aa95-404a-a2ce-41045cc180c7%2Fvu584hd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# MATH 1324 Written Assignment 2
## Section 4.6: Model and Solve Systems of Linear Equations Using Matrix Inverse Methods
### Problem Statement
Solve the following application using matrix inverse methods.
An international mining company has two mines in Voisey's Bay and Hawk Ridge. The composition of the ore from each field is given in the table:
| Mine | Nickel (%) | Copper (%) |
|---------------|------------|------------|
| Voisey's Bay | 2 | 4 |
| Hawk Ridge | 3 | 2 |
How many tons of ore from each mine should be used to obtain each order of nickel and copper in the table below:
| Metal | Order 1 | Order 2 |
|----------|---------|---------|
| Nickel | 6 tons | 8 tons |
| Copper | 8 tons | 8 tons |
### Solution
#### Step 1: Set Up the System of Equations
We can set up the linear system based on the given percentage compositions and required amounts:
For Nickel (N):
\[ 2x_1 + 3x_2 = \text{Nickel amount} \]
For Copper (C):
\[ 4x_1 + 2x_2 = \text{Copper amount} \]
Here,
- \( x_1 \) = amount of ore from Voisey's Bay
- \( x_2 \) = amount of ore from Hawk Ridge
#### Step 2: Turn the System into Matrix Form
Using the given orders,
- For order 1:
\[
\begin{bmatrix}
2 & 3 \\
4 & 2
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}
=
\begin{bmatrix}
6 \\
8
\end{bmatrix}
\]
- For order 2:
\[
\begin{bmatrix}
2 & 3 \\
4 & 2
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}
=
\begin{bmatrix}
8
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