Tuesday, December 9, 2008

Solution of a Homogeneous System of Linear Equations

AX = 0

In this case if A is nonsingular. X = 0 is the only solution. It is a trivial solution.

A system AX = 0 of n equations in n unknowns has non trivial solution iff the coefficieint matrix is singular.

To solve the system with singular A in 3 variables (as an example) Put z =k and solve the remaining equations for x and y in terms of k. This is the general solution to the problem.

A homogeneous system of linear equations is always consistent.

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