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The eigen values of a matirx are the values L such that Ax = Lx
where A is a matrix, x is a vector, and L is a constant.

The vector x is known as the eigenvector.

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Q: What is the echelon of a matrix?
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How do you find rank of a matrix?

First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.


How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row-echelon form?

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What is it when the first nonzero entry in each row of a matrix is one?

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How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row echelon form?

I bet it can be done, but I'll be darned if I can!


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Gaussian elimination as well as Gauss Jordan elimination are used to solve systems of linear equations. If, using elementary row operations, the augmented matrix is reduced to row echelon form, then the process is called Gaussian elimination. If the matrix is reduced to reduced row echelon form, the process is called Gauss Jordan elimination. In the case of Gaussian elimination, assuming that the system is consistent, the solution set can be obtained by back substitution whereas, if the matrix is in reduced row echelon form, the solution set can usually be obtained directly from the final matrix or at most by a few additional simple steps.


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