0.6 0.2 0.9 0.3 15 D = A = 14 X =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find the production schedule for the technology matrix and demand vector given below:

### Matrices in Linear Algebra

In this example, we have two matrices and a vector:

1. **Matrix \( A \)**:
   \[
   A = \begin{bmatrix} 
   0.6 & 0.2 \\ 
   0.9 & 0.3 
   \end{bmatrix}
   \]
   - This is a \(2 \times 2\) matrix.
   - The elements of the matrix are real numbers, representing coefficients that could be used in linear equations or transformations.

2. **Vector \( D \)**:
   \[
   D = \begin{bmatrix} 
   15 \\ 
   14 
   \end{bmatrix}
   \]
   - This is a \(2 \times 1\) vector.
   - The elements of the vector are constant terms from a system of linear equations or specific values applicable to a linear transformation.

3. **Matrix \( X \)**:
   \[
   X = \begin{bmatrix} 
   \_\_ \\ 
   \_\_ 
   \end{bmatrix}
   \]
   - This is a \(2 \times 1\) matrix, intended to hold unknown values.
   - The entries are placeholders for values that would result from solving the system of equations \(AX = D\).

This setup could be considered for solving a linear system of equations where matrix \( A \) contains the coefficients, matrix \( X \) holds variables to be solved, and vector \( D \) consists of the constants from each equation.
Transcribed Image Text:### Matrices in Linear Algebra In this example, we have two matrices and a vector: 1. **Matrix \( A \)**: \[ A = \begin{bmatrix} 0.6 & 0.2 \\ 0.9 & 0.3 \end{bmatrix} \] - This is a \(2 \times 2\) matrix. - The elements of the matrix are real numbers, representing coefficients that could be used in linear equations or transformations. 2. **Vector \( D \)**: \[ D = \begin{bmatrix} 15 \\ 14 \end{bmatrix} \] - This is a \(2 \times 1\) vector. - The elements of the vector are constant terms from a system of linear equations or specific values applicable to a linear transformation. 3. **Matrix \( X \)**: \[ X = \begin{bmatrix} \_\_ \\ \_\_ \end{bmatrix} \] - This is a \(2 \times 1\) matrix, intended to hold unknown values. - The entries are placeholders for values that would result from solving the system of equations \(AX = D\). This setup could be considered for solving a linear system of equations where matrix \( A \) contains the coefficients, matrix \( X \) holds variables to be solved, and vector \( D \) consists of the constants from each equation.
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