List of top Mathematics Questions on Time, Speed and Distance asked in GATE MA

Let \( A \) be a \( 2 \times 2 \) non-diagonalizable real matrix with a real eigenvalue \( \lambda \) and \( v \) be an eigenvector of \( A \) corresponding to \( \lambda \). Which one of the following is the general solution of the system \( y' = Ay \) of first-order linear differential equations?

Let \( A \) be a \( 3 \times 3 \) real matrix and \( b \) be a \( 3 \times 1 \) real column vector. Consider the statements:
1. The Jacobi iteration method for the system \( (A + \epsilon I_3)x = b \) converges for any initial approximation and \( \epsilon>0 \).
2. The Gauss-Seidel iteration method for the system \( (A + \epsilon I_3)x = b \) converges for any initial approximation and \( \epsilon>0 \).
Which one of the following is correct?