One or more may be wrong. I need help with these questions.. You can only answer

Question

One or more may be wrong. I need help with these questions..

You can only answer one of them if you wish, but I would like to know when an augmented matrix has one, none, or infinitely many solutions so I could answer the remaining ones.

Thank you!

10-15 10 01 00 00 01 A. No solutions o B. Infinitely many solutions O C. Unique solution D. None of the above 2. 101 9 01 12 001 0 A. No solutions o B. Infinitely many solutions C. Unique solution D. None of the above 010-13 00111 A. Unique solution o B. No solutions o C. Infinitely many solutions D. None of the above 4. 100 18 001 -16 O A. No solutions o B. Infinitely many solutions C. Unique solution D. None of the above

Explanation / Answer

Ans(1):
given augmented matrix is already in reduced row echelon form which corresponds to system
1 x1   -15 x3 = 0
1 x2   = 0
    0 = 1
    0 = 0

we see that third equation 0=1 is clearly FALSE.
so the system has NO solution.
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so basically if you get FALSE condition then that means NO solution:
True condition like 0=0 without any false equation then that indicates Infinitely many solution.
If none of above both cases then that's unique solution:)

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