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Matrices and equations

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1. Guassian Elimination is really just using the regular Elimination Method and applying the Triangular Form procedures to a set of linear equations, but without having to write down all the variables in the equations each time. This in itself simplifies the procedure and helps focus on the task. What is the ultimate goal of all these methods and procedures?

2. If you had 5 linear equations using 5 variables, what would the augmented matrix look like? What would this matrix look like in echelon form?

3. What does the final row of the augmented matrix in echelon form (the above description) tell you about the solution to the system of 5 linear equations?

4. Is it always possible to take any square matrix and write it in echelon form with all 1's along its main diagonal?

5. Can you take any two matrices and add them, subtract them and multiply them together?

6. Is it possible to divide two matrices?

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Solution Summary

The solution explains how matrices are used to solve equations, and also explains matrix operations.

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1. Guassian Elimination is really just using the regular Elimination Method and applying the Triangular Form procedures to a set of linear equations, but without having to write down all the variables in the equations each time. This in itself simplifies the procedure and helps focus on the task. What is the ultimate goal of all these methods and procedures? Guassian elimination will allow us eliminate unknowns, which will in turn led to us arriving at a system that is easily solvable. This procedure is used to determine whether or not the set of linear equations will have unique solution, no solution, infinitely many solutions. [Unique solution is defined as there exist one and only one set of values that ...

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