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Competitive Stats
Q32Section B (Section B)32 of 60

How many parameter pairs give infinite solutions

Let a,b∈Ra,b\in\mathbb{R}. Consider the system of linear equations x+y+3z=5,ax−y+4z=11,2x+by+z=3.x+y+3z=5,\qquad ax-y+4z=11,\qquad 2x+by+z=3. Then which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.