MTH603 Quiz 1 Solution and Discussion

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While using power method, from the resultant normalize vector
u(2)=11.4817⎛⎝⎜⎜0.3981760.8212671.0⎞⎠⎟⎟we have the largest eigen value and the corresponding eigenvector as

How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?

While using Gaussian Elimination method, which of the following augmented matrix is in upper triangular form?

Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?

The eigenvectors of a square matrix are the nonzero vectors that, after being multiplied by the matrix, remain …………… to the original vector.

The GaussSeidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
The GaussSeidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices. Explanation: GaussSeidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices because only in this case convergence is possible.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
The Jacobi method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal (Bronshtein and Semendyayev 1997, p. 892). Each diagonal element is solved for, and an approximate value plugged in. The process is then iterated until it converges.

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?
Finite Multiple
Infinite many
Unique
None 
While using the relaxation method for finding the solution of the following system
11x1+x2−x3=8
x1+8x2+5x3=9 with the initial vector (0,0,0), the residuals would be
x1+x2+9x3=7 
Jacobi’s method is highly recommended for ………… matrix to compute all the Eigen values and the corresponding eigenvectors.
Real symmetric
Non real symmetric
real unsymmetric
non of given 
@zareen said in MTH603 Quiz 1 Solution and Discussion:
Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?

Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?

@zareen said in MTH603 Quiz 1 Solution and Discussion:
The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.
NO

The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.
no
atleast one