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Question

If the system of linear equations
x1+2x2+3x3=6
x1+3x2+5x3=9
2x1+5x2+ax3=b
is consistent and has infinite number of solutions, then?

A
aR{8} and bR={15}
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B
a=8, b can be any real number
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C
a=8,b=15
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D
b=15, a can be any real number
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Solution

The correct option is C a=8,b=15
For consistent and has infinite Number of solution, we have to create linear equations such that it is less then Number of unknown.
now, x1+2x2+3x3=6(1)
x1+3x2+5x3=9(2)
2x1+5x2+ax3=b(3)
now, here adding (1) & (2) get equation (3), so,
2x1+5x2+8x3=15(4)
now, compare equation (3) & (4).
a=8 & b=15
For Consistent and Infinite Number of solution a=8 & b=15.

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