Consider the following system of linear equations. 2x1 + 3x2 + 4x3 + x4 14 4x1...

 

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Consider the following system of linear equations. 2x1 + 3x2 + 4x3 + x4 14 4x1 + 1x2 + 1x3 + 5x4 = 23 1x1 + 2x2 + 1x3 + 6x4 = 29 = (a) (5) State all basic solutions with their associated basic matrix B. (b) (10) For the basic solution x= (x1, X2, X3, x4) obtained with B=[a2,A3,A4], i.e., the last three columns of matrix A of the linear system above, generate two other distinct nonbasic solutions x' and x" such that x=0.5x'+0.5x". Consider the following system of linear equations. 2x1 + 3x2 + 4x3 + x4 14 4x1 + 1x2 + 1x3 + 5x4 = 23 1x1 + 2x2 + 1x3 + 6x4 = 29 = (a) (5) State all basic solutions with their associated basic matrix B. (b) (10) For the basic solution x= (x1, X2, X3, x4) obtained with B=[a2,A3,A4], i.e., the last three columns of matrix A of the linear system above, generate two other distinct nonbasic solutions x' and x" such that x=0.5x'+0.5x".

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