For what value of λ the system [1 3, 3 λ][x y] = [1 3] has infinitely many solutions?
- λ = 9
- λ = 6
- λ = 8
- None of these
Explanation
Let's directly evaluate the system of equations:
1x + 3y = 1
3x + λy = 3
For infinitely many solutions, these equations must represent the same line. Multiplying the first equation by 3 gives:
3x + 9y = 3
Comparing this with the second equation 3x + λy = 3, we see that λ must equal 9 for the equations to be identical.
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