Better Students Ask More Questions.
Does a homogeneous system of 4 equations in 5 variables have infinitely many...
2 Answers | add yours
High School Teacher
Because the matrix corresponding to coefficients of the variables has its rank less than the number of variables. In such a case at least one variable will be free variable and hence can take infinitely many values from corresponding field.
Posted by rakesh05 on March 17, 2013 at 9:30 AM (Answer #1)
Homogeneous systems of linear equations are systems where the constant term in each equations is zero. Therefore, they have the form [A|0], where A is the matrix of coefficients of the variables in the system of equations. Systems of this type always have a solution. There is always the trivial solution where [x1, x2, ..., xn] = [0,0,...0].
Apart from this ,we four equation in 5 variables, which means we have one free variables and we can assign any arbitrary value to it . This implies we have an infinite no. of solutions.
Posted by pramodpandey on March 17, 2013 at 12:29 PM (Answer #2)
Join to answer this question
Join a community of thousands of dedicated teachers and students.