SOLUTION: Q) Consider the system of linear equations x + 3y = 5 2x + ay = b where a and b are real numbers (a) Write out the augmented matrix for

Question 1021868: Q) Consider the system of linear equations
x + 3y = 5
2x + ay = b where a and b are real numbers

(a) Write out the augmented matrix for this system of linear equations.
(b) Use elementary row operations to reduce the augmented matrix to row-echelon form.
(c) Determine for what values of a and b does the system have infinitely many solutions.
(d) Determine for what values of a and b does the system have no solution.
(e) Determine for what values of a and b does the system have an unique solution.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) augmented matrix
1 3 5
2 a b
****************************
b) row-echelon form
:
R2 - 2R1
1 3 5
0 a-6 b-10
*****************************
c) infinitely many solutions
leading variable is x1
x2 is free variable if a is not = 7, b any real
*****************************
d) no solutions
a=6 and b=10
****************************
e) unique solution
a=7, b any real
***************************8

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