Linear Algebra Conditions such that x+by=-1, 2ax+2y=5 has exactly 1 soln

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Conditions such that x+by=-1, 2ax+2y=5 has exactly 1 soln

The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D
 
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Subhotosh Khan

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The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

What have you been taught about conditions for -

infinite number of solutions,

No solution and

Unique solution

For a set of linear equations with multiple variables (also known as "unknown").
 
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stapel

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Find conditions on a and b such that the following system has exactly one solution:

. . . . . . .x + by = -1

. . . . .2ax + 2y = 5

The answers is ... "ab ≠ 1", but I have no clue how to get to that answer.
What did you get when you tried to solve the system? For instance, you solved the first equation for "x=", plugged this into the second equation, solved for "y=", and... then what?

Please be complete. Thank you! ;)
 

MarkFL

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I just wanted to post to say that this same question was cross-posted at the math help site I help administrate, where HallsofIvy provided good help. :D
 
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The answer

Thanks everyone for replies.

This can easily be done with determinants. If a square matrix's determinant does not equal zero, then that square matrix will have an inverse hence having a unique solution. Since this is a 2x2 matrix, just compute the determinant with the condition that it cannot equal zero
(1)(2)-(2ab) =/= 0
2 =/= 2ab
1=/= ab
 
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