linear equations Find the values of a and b such that the sy

linear equations. Find the values of a and b such that the system has:

a. A unique solution

b. A two-parameter solution

Let (a 0 b 2 a a 4 4 0 a 2 b) be the augmented matrix for a system of linear equations. Find the values of a and b such that the system has: A unique solution A two-parameter solution

Solution

unique solution:

ax+bz=2

ay+2z=b

a(x+y)+4z=4

so we get

z=1

x=(2-b)/a

y=(b-2)/a

so unique solution will exist if we take a not equal to zero.

two parameter solution:

since solution to this problem is

z = 1

y = t

x = -t

so we don\'t have any value of a and b such that this has two parameter solution.As we have only one parameter t.