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)

The horizontal lines in a matrix are called the ____ of the matrix.

• A) columns
• B) rows
• C)
• D)

Let A, B and C matrices are of same order and (A+B)+C=A+(B+C), this law is known as

• A) Associative law
• B) Distributive law
• C) Commutative law
• D) Cranmer's rule

\begin{gathered} {\text{The}} {\text{Elementary Row operations:}}R_2^/ \to {R_2} + 4{R_1} ~{\text{and}}~ R_3^/ \to {R_3} - 6{R_1} ~{\text{are }} \ {\text{performed on}}~ {\text{to}} ~{\text{get}} \left( {\begin{array}{*{20}{c}} 1&2&{ - 5} \\\ { - 4}&1&{ - 6} \\\ 6&3&{ - 4} \end{array}} \right) \sim - - - - - - ? \\\ \end{gathered}

• A) \left( {\begin{array}{*{20}{c}} 1&2&{ - 5} \\\ 0&9&{ - 26} \\\ 0&{ - 9}&{26} \end{array}} \right)
• B) \left( {\begin{array}{*{20}{c}} 1&2&{ - 5} \\\ 0&{ - 9}&{ - 26} \\\ 0&{ - 9}&{26} \end{array}} \right)
• C) \left( {\begin{array}{*{20}{c}} 1&2&{ - 5} \\\ 0&9&{26} \\\ 0&{ - 9}&{ - 26} \end{array}} \right)
• D) \left( {\begin{array}{*{20}{c}} 1&2&{ - 5} \\\ 0&{ - 9}&{26} \\\ 0&9&{ - 26} \end{array}} \right)

If the augmented matrices of two linear systems are row equivalent, then the two systems have the same _______.

• A) columns
• B) rows
• C) solution set
• D) elements

The transpose of the product of two matrices is equal to

• A) $(AB)^{T}=A^{T}B^{T}$
• B) $(AB)^{T}=B^{T}A^{T}$
• C)
• D)

\begin{gathered} {\text{If the equation:}}\left( {\begin{array}{*{20}{c}} { - 2}&3 \\ 5&1 \end{array}} \right)\left( {\begin{array}{*{20}{c}} x \\ y \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {{b_1}} \\ {{b_2}} \end{array}} \right){\text{has the solution for all }} {b_1},{b_2} \in \mathbb{R}, \ {\text{then}} \left( {\begin{array}{*{20}{c}} { - 2} \\ 5 \end{array}} \right) {\text{and}} \left( {\begin{array}{*{20}{c}} 3 \\ 1 \end{array}} \right) {\text{will span}} - - - - - . \\ \end{gathered}

• A) {\mathbb{R}^3}space
• B) \mathbb{R}~space
• C) {\text{Nothing}}
• D) {\mathbb{R}^2}space

A set of two vectors \{ {v_1},{v_2}\} is linearly dependent if and only if one of the vector is

• A) Additive inverse of the other
• B) Multiple of the other
• C)
• D)