top of page # In the matrix form above system of equation is written as:

Linear System of Equations # Vector X is such that on linear transformation with matrix M, it lands on vector D. # Here X is unknown while D and M are known. So if we perform inverse transformation of M on D, we can find X. • # If vector D lies on the same line as iT and jT, then system of equation has infinitely many solution.

Consistency of system • # If vector D does not lie on the same line as iT and jT, then system of equation is inconsistent amd no solution exists. • # iT and jT (unit vector i and j after transformation) remain in one plane but are not collinear. Number of dimension in the output of transformation is 2, hence rank is 2.

Rank  • # iT and jT become collinear after transformation. No of dimension in the output is reduced to 1, hence rank is 1.  • # iT and jT are reduced to a point after linear transformation. Since origin remain fixed in linear transformation, hence iT and jT both shift to origin. For this case rank of the matrix is zero.  # Consider a linear system of equation MX = D. For this system augmented matrix MA is defined as # D) 4

Previous years questions # Solution: Consider a 3x4 real matrix A as: # Solution: Consider matrix A and B as  # D) √2 # where; # For a = 4, augmented matrix A:D is # Convert to echelon form    # Similarly for a = -3, augmented matrix A:D in echelon form is # GATE 2016: The solution to the system of equations as given below is # Solution: For system of equation Ax = B, x is found out by # Matrix of cofactors of A  # Inverse of A  # where; # Augmented matrix A:B is # Echelon form of A:B is # Solution: System of equation in matrix form is written as # Solution: System of equation in matrix form Ax = B is written as: # Augmented matrix A:B is written as # Augmented matrix in echelon form is bottom of page