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

Direct methods can be more rapid than iterative algorithms.

• A) False
• B) True
• C)
• D)

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

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

A partitioned matrix is a partition of a matrix into rectangular smaller matrices called _____.

• A) Column
• B) Element
• C) Row
• D) Blocks

A sufficient condition for the Jacobi’s method to converge for the linear system Ax=b

• A) None of the above.
• B) A is non-singular
• C) A is diagonally dominant
• D) A-I is diagonally dominant

What is the maximum possible number of pivots in a 6x6 matrix ?

• A) 0
• B) 4
• C) 2
• D) 6

{\text{If }}A = \left( {\begin{array}{*{20}{c}} 1&2 \\\ 3&4 \end{array}} \right)\mathop \sim \limits^{{\text{Row Equivalent}}} \left( {\begin{array}{*{20}{c}} 1&0 \\\ 0&1 \end{array}} \right), {\text{then the Columns of}} ~{\text{A}}~ {\text{are}}~ {\text{Linearly}} {\text{ - - - - - - - }}

• A) Dependent
• B) Independent
• C)
• D)

{\text{Set}} \left\{ {\left( {\begin{array}{*{20}{c}} 1 \\\ 2 \end{array}} \right),\left( {\begin{array}{*{20}{c}} 0 \\\ 0 \end{array}} \right)} \right\} {\text{is Linearly - - - - - in}}~ {\mathbb{R}^2}.

• A) Independent
• B) Dependent
• C)
• D)

\begin{gathered} {\text{What will be the order of matrix:}} A - B{\text{, if the orders of both}} ~ \ A ~{\text{and}} ~B ~{\text{is}}~ 2 \times 3? \\\ \end{gathered}

• A) 3 \times 3
• B) 2 \times 3
• C) 0 \times 0
• D) 2 \times 2

\begin{gathered} {\text{Under which of the following condition, a system of Linear Equations whose }} \ {\text{Row - Reduce form is }}\left( {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 1 \\\ 0 \end{array}}&{\begin{array}{*{20}{c}} 2 \\\ 0 \end{array}}&{\begin{array}{*{20}{c}} | \\\ | \end{array}}&{\begin{array}{*{20}{c}} { - 1} \\\ {h - 3k} \end{array}} \end{array}} \right){\text{ has }}~Infinite ~{\text{many}} ~{\text{solutions?}} \\\ \end{gathered}

• A) h = 3k
• B) \left( {h,k} \right) \ne \left( {0,0} \right)
• C) \left( {h,k} \right) = \left( {0,0} \right)
• D) h \ne 3k

$\left[ {\begin{array}{*{20}{c}} 3 \\\\ 2 \\\\ { - 1} \end{array}} \right] \times \left[ {\begin{array}{*{20}{c}} 8&{ - 4}&5 \end{array}} \right] = $

• A) 11
• B) $\left[ {\begin{array}{*{20}{c}} {24}&{ - 8}&{ - 5} \end{array}} \right]$
• C) $\left( {\begin{array}{*{20}{c}} {24}&{ - 12}&{15} \\\\ {16}&{ - 8}&{10} \\\\ { - 8}&4&{ - 5} \end{array}} \right)$
• D) $\left[ {\begin{array}{*{20}{c}} {24} \\\\ { - 8} \\\\ { - 5} \end{array}} \right]$

{\text{Which of the following is Row - Equivalent of}} \left( {\begin{array}{*{20}{c}} 3&2 \\\ 1&2 \end{array}} \right)?

• A) \left( {\begin{array}{*{20}{c}} 1&2 \\\ 0&{ - 4} \end{array}} \right)
• B) \left( {\begin{array}{*{20}{c}} 1&2 \\\ 2&3 \end{array}} \right)
• C) \left( {\begin{array}{*{20}{c}} 1&2 \\\ 0&4 \end{array}} \right)
• D) \left( {\begin{array}{*{20}{c}} 1&2 \\\ { - 4}&0 \end{array}} \right)

{\text{For the matrix:}}~ A = \left( {\begin{array}{*{20}{c}} 4&{x + 2} \\\ {2x - 3}&{1} \end{array}} \right), {\text{if}} ~A = {A^t}, {\text{then}} ~x = - - - .

• A) -5
• B) Undefined
• C) 5
• D) 5/2

{\left( {\begin{array}{*{20}{c}} {Cos\theta }&{Sin\theta } \\\ { - Sin\theta }&{Cos\theta } \end{array}} \right)^{ - 1}} =

• A) b) \left( {\begin{array}{*{20}{c}} { - Cos\theta }&{Sin\theta } \\\ {Sin\theta }&{Cos\theta } \end{array}} \right)
• B) c) \left( {\begin{array}{*{20}{c}} {Cos\theta }&{Sin\theta } \\\ {Sin\theta }&{ - Cos\theta } \end{array}} \right)
• C) d) \left( {\begin{array}{*{20}{c}} {Cos\theta }&{ - Sin\theta } \\\ {Sin\theta }&{Cos\theta } \end{array}} \right)
• D) a) \left( {\begin{array}{*{20}{c}} {Cos\theta }&{Sin\theta } \\\ { - Sin\theta }&{Cos\theta } \end{array}} \right)