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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 34E
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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
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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