# MTH603 Grand Quiz Solution and Discussion

• Gauss–Seidel method is also known as method of …………….

• Differences methods are iterative methods. yes or no

1. Which of the following is not an iterative method? Explanation: Jacobi’s method, Gauss Seidal method and Relaxation method are the iterative methods and Gauss Jordan method is not as it does not involves repetition of a particular set of steps followed by some sequence which is known as iteration.

• Differences methods are iterative methods. yes or no

• Power method is applicable if the eigen vectors corresponding to eigen values are linearly _______.

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal. Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

• Power method is applicable if the eigen vectors corresponding to eigen values are linearly _______.

• Two matrices with the same characteristic polynomial need not be similar.

Two similar matrices have the same characteristic polynomial. The converse however is not true in general: two matrices with the same characteristic polynomial need not be similar. The matrix A and its transpose have the same characteristic polynomial. … In this case A is similar to a matrix in Jordan normal form.

• Two matrices with the same characteristic polynomial need not be similar.

• If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

The eigenvalues of B are 1,4,6 since B is an upper triangular matrix and eigenvalues of an upper triangular matrix are diagonal entries. We claim that the eigenvalues of A and B are the same.

• If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

• If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

Since similar matrices A and B have the same characteristic polynomial, they also have the same eigenvalues. If B = PAP−1 and v = 0 is an eigenvector of A (say Av = λv) then B(Pv) = PAP−1(Pv) = PA(P−1P)v = PAv = λPv. Thus Pv (which is non-zero since P is invertible) is an eigenvector for B with eigenvalue λ.

The matrix B has the same A as an eigenvalue. M−1x is the eigenvector. If two matrices are similar, they have the same eigenvalues and the same number of independent eigenvectors (but probably not the same eigenvectors).

• If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

Since similar matrices A and B have the same characteristic polynomial, they also have the same eigenvalues. If B = PAP−1 and v = 0 is an eigenvector of A (say Av = λv) then B(Pv) = PAP−1(Pv) = PA(P−1P)v = PAv = λPv. Thus Pv (which is non-zero since P is invertible) is an eigenvector for B with eigenvalue λ.

• If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

• The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal. Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

• The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

• The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

Explanation: Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices because only in this case convergence is possible. … This is the modification made to Jacobi’s method, which is now called as Gauss-seidal method.

• The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

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