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    Square Matrix with Determinant Equal to 0 and Basis for a Solution Space

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    1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax=b then every solution to this equation must have the form x=X+xot where xo is a solution of Ax=0.

    2) Find a basis for the solution space of the following system of equations.
    x- 2x2+ x3 =-4
    -2x +3x2 + x4=6
    3x -3x2 -3x3 -12x4=-6
    -3x +5x2 -x3 +4x4=10

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    Solution Preview

    1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax = b then every solution to this equation must have the form x = X + xo where xo is a solution of Ax = 0.
    Since x0 is a solution to Ax = 0, we have Ax0 = 0 ......(i)
    Since X is ...

    Solution Summary

    A square matrix with determinant equal to 0 and a basis for a solution space are investigated. The solution is detailed and well presented.

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