Q.

The number of solutions of the system of equations 2x+y–z=7, x–3y+2z=1, x+4y–3z=5 is

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a

3

b

2

c

1

d

0

answer is D.

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Detailed Solution

he augmented matrix is 21-171-32114-35 R2→2R2-R1 ,R3→2R3-R1 =21-170-75-507-53 R3→R3+R2 =21-170-75-5000-2from last row the equation is 0x+0y+0z=-2 which is a contradiction so the system of equations is inconsistent and it has no solution
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The number of solutions of the system of equations 2x+y–z=7, x–3y+2z=1, x+4y–3z=5 is