1. The problem statement, all variables and given/known data
In Exercises 49 and 50, find values of a, b, and c(if possible) such that the system of linear equations has (a) a unique solution, (b) no solution, and (c) an infinite number of solutions.
49.
[itex]x+y ~ = 2[/itex]
[itex]~y+z =2[/itex]
[itex]x+ ~ z =2[/itex]
[itex]ax + by + cz=0[/itex]
2. Relevant equations
3. The attempt at a solution
I immediately recognized this system as one consisting of planes. Hence, wouldn't it be impossible for there to exist a unique solution, as my geometric intuition of the situation ?
In Exercises 49 and 50, find values of a, b, and c(if possible) such that the system of linear equations has (a) a unique solution, (b) no solution, and (c) an infinite number of solutions.
49.
[itex]x+y ~ = 2[/itex]
[itex]~y+z =2[/itex]
[itex]x+ ~ z =2[/itex]
[itex]ax + by + cz=0[/itex]
2. Relevant equations
3. The attempt at a solution
I immediately recognized this system as one consisting of planes. Hence, wouldn't it be impossible for there to exist a unique solution, as my geometric intuition of the situation ?
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