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How to find how many linearly independent eigen vectors are possible of a matrix?

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How to find how many linearly independent eigen vectors are possible of a matrix?

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To find out the no of linearly independent vectors , first find the rank of the matrix , so no of linearly independent vectors=n-r where n is the no of unknowns and r is the rank of the matrix .

Now for calculating the value of unknowns u should first try converting the matrix to echelon form and then try calculating the unknowns.

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