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Are all homogeneous systems inconsistent?

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bleeeeee | Student | (Level 1) Honors

Posted March 5, 2013 at 4:47 AM via web

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Are all homogeneous systems inconsistent?

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 17, 2013 at 9:30 AM (Answer #1)

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No ,

because Homogeneous systems of linear equations are systems where the constant term in each equations is zero. Therefore, they have the form [A|0], where A is the matrix of coefficients of the variables in the system of equations. Systems of this type always have a solution. There is always the trivial solution where [x1, x2, ..., xn] = [0,0,...0].

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