The Jacobi’s iteration converges if a square matrix A is diagonally dominant.

• A) False
• B) True
• C)
• D)

If $X = \left[ \begin{array}{l} \,M\\\N\, \end{array} \right]\,\,{\rm{and}}\,\,Y = \left[ {\,Q\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,P\,} \right]$ ( where $M$ , $N$ , $Q$ and $P$ are square sub-matrices of same size ) , then which of the following is possible ?

• A) The product $XY$ and $YX$ both are defined.
• B) The product $XY$ and $YX$ both are not defined.
• C) The product $XY$ is not defined but $YX$ is defined.
• D) The product $XY$ is defined but $YX$ is not defined.

As soon as an approximate solution of a linear system is sufficiently accurate for practical work then which of the following is true for an iterative process?

• A) The process may be stopped.
• B) The reduced row-echelon method may be used.
• C) The row-echelon method may be used.
• D) The process may be carried on.

In LU-decomposition, if A is the square matrix of order m, then the order of both lower and upper triangular matrices will be ______.

• A) $m+1$
• B) $m$
• C) $2m$
• D) $m^2$

If a system of equations is solved using the Gauss-Seidel method, then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix ?

• A) All of its entries below and above the diagonal must be zero.
• B) All of its entries above the diagonal must be zero.
• C) All of its entries below the diagonal must be zero.
• D) All of its entries on the diagonal must be zero.

The Gauss-Seidel method is applicable to strictly _________ dominant matrix.

• A) column wise
• B) row wise
• C) diagonally
• D) both row and column wise

A matrix in which each descending diagonal from left to right is constant is called a _____ matrix.

• A) diagonal
• B) diagonal-constant
• C) block upper triangular
• D) block lower triangular

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

• A) No
• B) Two
• C) more than two
• D) more than two

In Jacobi’s method, the rate of convergence is quite ---------- compared with other methods.

• A) None of these
• B) Slow
• C) Fast
• D) Speedy

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

• A) True
• B) False
• C)
• D)

A partitioned matrix ‘A’ is said to be block diagonal if the matrices on the main diagonal are square and all other position matrices are ______.

• A) Unit
• B) Nonzero skew symmetric
• C) Nonzero symmetric
• D) Zero

LU-decomposition converts the problem of solving the single system A x = b into the problem of solving the two systems, L y = b and U x = y, these systems are easy to solve because their co-efficient matrices are_______.

• A) Identity
• B) Diagonal
• C) Identity
• D) Triangular

If a square matrix A can be reduced to row echelon form with _____ interchanges, then A has an LU-decomposition.

• A) No row
• B) Row
• C) Column
• D) No column

If A is strictly diagonally dominant matrix, then which of the following is true for A?

• A) It is a singular matrix.
• B) It is a rectangular matrix.
• C) It is an invertible matrix.
• D) It is a null matrix.

A decomposition of a matrix as a product of two or more matrices is called the matrix _____.

• A) Transformation
• B) Factorization
• C) Multiplication
• D) Composition

At what condition when both the Jacobi and Gauss-Seidel sequences converge to the unique solution of Ax = b, for any initial ?

• A) When A is symmetric
• B) When A is scalar
• C) When A is invertible
• D) When A is singular

If the absolute value of each diagonal entry in a square matrix exceeds the sum of the absolute values of the other entries in the same row, then which of the following is true for the matrix?

• A) It is a strictly diagonally dominant matrix.
• B) It is a null matrix.
• C) It is a singular matrix.
• D) It is a diagonally dominant matrix.

For which of the matrix, the Gauss-Seidel method is applicable?

• A) Null matrix
• B) Diagonally dominant matrix
• C) Strictly diagonally dominant matrix
• D) Rectangular matrix

If A is strictly diagonally dominant, then A is _________.

• A) invertible
• B) scalar
• C) singular
• D) symmetric

How many assumptions are there in Jacobi’s method?

• A) 5
• B) 4
• C) 2
• D) 3