Suppcsc a4x3 coem cient matrix fora system has four pivot coluns. Is the systom

Question

Suppcsc a4x3 coem cient matrix fora system has four pivot coluns. Is the systom consistent? Why or why not? Choosc the corct answer below OA. There is at leas ons tow of the coefmicienl maik thal dos nol have a pivot posilion. This means the ausgmenloed matix, which will have nine colurmms, cculd trave a row of the form 0 0 0 s the system coua'd be inconsistent OB. Theis a least ore low of e cu ic ent rna ux hal d es ru have a p po lion his means u u r ented mat x, which wil have n ng columns must have r w o the form o o o o o o o o so e s s em s nuons lent. O C. There is a piot postion in each row at the coetticient matrx. The augmented matnx will nave nine calumns and will not have a row ot the torm D 11, s the system is cons stent l here is a piwot pasition in each o at he costhcient matrix lhe augmented atr x wil have hve cumns and wil not have a row o the arm () (1 0 1 the system is consistent

Explanation / Answer

Correct option:

C.

Thee is a pivot position in each row of the coefficient matrix. The augmentated matrix will have nine columns and will not have a row of the form {0 0 0 0 0 0 1} , so the system is consistent.

EXPLANATION:

Given: 4X8 coefficient matrix. The system has 4 pivot columns.

With 4 pivots, there must be a pivot in the fourth (bottom) row of the cofficiet matrix. The reduced echelon form

[0 0 0 0 0 0 0 0 1]

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