Let be the coefficient matrix of a system of two linear equations in two variables
MATHEMATICS · Single correct · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables
Problem
Let A=(1224) be the coefficient matrix of a system of two linear equations in two variables. Which one of the following statements is TRUE about the system?
(a) The system necessarily has a unique solution because detA=8=0.
(b) Since the coefficient matrix is singular, the system must always have infinitely many solutions irrespective of the constants.
(c) The system cannot have a unique solution; it may have infinitely many or no solution depending on the constant terms.
(d) Because the rows of A are proportional, the system can never be consistent; hence it has no solution.