Homework Soursea system of four equations in four unknowns can have at most
a system of four equations in four unknowns can have at most one solution. True or false? As long as there is a situation that the set has only one solution then it\'s true
a system of four equations in four unknowns can have at most one solution. True or false? As long as there is a situation that the set has only one solution then it\'s true
a system of four equations in four unknowns can have at most one solution. True or false? As long as there is a situation that the set has only one solution then it\'s true
Solution
It is false. Because some times the system has infinitely many solutions.
For example,
x+y+z+w=6
x=1
y=2
2x+y=4
If we try to solve this we get,
x=1, y=2 and 1+2+z+w=6
Then we get
x=1, y=2 amd z+w=3
Let us assume that w= t , where t is a real number.
Then, z+t=3. So, z= 3-t
So the solution system is,
x=1, y=2, z=3-t and w=t, where t is a real number.
Since there are infinitely many real numbers, this system has infinitely many solutions.
