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Question

The number of solutions of the system of equations:
2x + y − z = 7
x − 3y + 2z = 1
x + 4y − 3z = 5
(a) 3
(b) 2
(c) 1
(d) 0

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Solution


(d) 0The given system of equations can be written in matrix form as follows: 21-11-3214-3xyz=715AX=BHere, A= 21-11-3214-3, X=xyz and B=715Now,A=2 9-8-1-3-2-14+3 =2+5-7 =0Let Cij be the cofactors of the elements aij in A=aij. Then,C11=-11+1-324-3=1, C12=-11+2121-3=5, C13=-11+3 1-314=7C21=-12+11-14-3=-1, C22=-12+22-11-3=-5, C23=-12+32114=-7C31=-13+11-1-32=5, C32=-13+22-112=-5, C33=-13+3211-3=-7adj A=157-1-5-75-5-7T= 1-155-5-57-7-7adj AB=1-155-5-57-7-7715=7-1+2535-5-2549-7-35=3256≠ 0The given system of equations is inconsistent. Thus, it has no solution.

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