SOLUTION: Which is true A.The system x + 3y + z = 0 2x - 4y + z = 0 7x + y + 7z = 0 has infinitely many solutions. B. if the determinant of the coefficient matrix

Algebra ->  Matrices-and-determiminant -> SOLUTION: Which is true A.The system x + 3y + z = 0 2x - 4y + z = 0 7x + y + 7z = 0 has infinitely many solutions. B. if the determinant of the coefficient matrix      Log On


   

Question 721628: Which is true
A.The system x + 3y + z = 0
2x - 4y + z = 0
7x + y + 7z = 0
has infinitely many solutions.
B. if the determinant of the coefficient matrix of a non-homogeneous system is 0 then the system has no solution.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Short answer: Neither is true.

If the determinant of the coefficient matrix is zero, then the system either has no solutions or an infinite number of solutions.

A. False. The determinant of the coefficient matrix for this system works out to be -20. So it has a single solution.

B. False. The statement is missing the "or an infinite number of solutions" part. (This might considered true if "no solution" was interpreted to mean "no single solution" or something to that effect.)