Find the production schedule for the technology matrix and demand vector given below: ### Matrices in Linear AlgebraIn 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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Answered: 0.6 0.2 0.9 0.3 15 D = A = 14 X =

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

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.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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