Question: * 7. (a) Define the terms basic variable and free variable. (b) Use Gauss-Jordan elimination to solve each of the following homogeneous systems: x1+x2 -

* 7. (a) Define the terms basic variable and free variable. (b) Use Gauss-Jordan elimination to solve each of the following homogeneous systems: x1+x2 - 4x3 = 0 1 + 2 02 - 23 O (i) x1 + 3x2 - 4x3 = 0 (ii) x2 + 4x3 = 0 3x2 + 23 = 0 x1 + 3x2 + 3x3 = 0 (c) In each case, find (by inspection or otherwise) a particular solution of the system, and hence write down the general solution, using the results of (b). x1+ x2 -4x3 = 8 x1 + 2x2 - X3 (i) x1 + 3x2 - 4x3 = 8 (ii) x2 + 4x3 = 1 3x2 + 23 = -2 x1 + 3x2 + 3x3 = 4 Verify your answer in MATLAB using the rref and A b commands

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