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)

\left( {\begin{array}{*{20}{c}} { - 1}&0 \\\ 0&{ - 1} \end{array}} \right)

• A) \frac{{ - 2}}{3} {\text{and }} \frac{1}{3}
• B) \frac{2}{3} {\text{and }} \frac{1}{3}
• C) \frac{{ - 2}}{3} {\text{and }} \frac{{ - 1}}{3}
• D) \frac{{ - 2}}{3} {\text{and }} \frac{{ - 1}}{3}

The vertical lines in a matrix are called the _____ of the matrix.

• A) columns
• B) rows
• C)
• D)

{\text{If}} ~\alpha = \beta , {\text{then}}~ \left| {\begin{array}{*{20}{c}} {Cos\alpha }&{ - Sin\alpha } \\\ {Cos\beta }&{Sin\beta } \end{array}} \right| =

• A) Cos2\alpha
• B) Undefined(\infty )
• C) 1
• D) Sin2\alpha

\begin{gathered} The ~values~ of~ x~ and~ y~ which~ satisfy~ the ~matrix~ equation: \ \left( {\begin{array}{*{20}{c}} 4 \\\ y \end{array}} \right) = x\left( {\begin{array}{*{20}{c}} 2 \\\ 3 \end{array}} \right) are - - - - . \\\ \end{gathered}

• A) \left( {\begin{array}{*{20}{c}} x \\\ y \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 2 \\\ 6 \end{array}} \right)
• B) \left( {\begin{array}{*{20}{c}} x \\\ y \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 3 \\\ 2 \end{array}} \right)
• C) \left( {\begin{array}{*{20}{c}} x \\\ y \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 2 \\\ 3 \end{array}} \right)
• D) \left( {\begin{array}{*{20}{c}} x \\\ y \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 6 \\\ 2 \end{array}} \right)

A matrix with equal number of rows and columns is called _____ matrix.

• A) rectangular
• B) row
• C) column
• D) square

$${\text{If}} ~~i= \sqrt { - 1} \in \mathbb{C}, {\text{and}}~~ n \in {\mathbb{Z}^ + }, {\text{then}} ~~{\left( {\begin{array}{*{20}{c}} i&0 \\\ 0&i \end{array}} \right)^{4n}} = - - - - - - .$$

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

If \[A = \left[ {\begin{array}{*{20}{c}} 2&{ - 7} \\\\\\ 4&3 \end{array}} \right]\], then adjoint of A is

• A) \[A = \left[ {\begin{array}{*{20}{c}} 2& 7 \\\\\\ {-4}&3 \end{array}} \right]\]
• B) \[A = \left[ {\begin{array}{*{20}{c}} 3& 7 \\\\\\ {-4}&2 \end{array}} \right]\]
• C)
• D)

If an augmented matrix $[A \,\ b]$ has a pivot position in every row then

• A) The equation$Ax=b$ may or may not be consistent
• B) The equation$Ax=b$ may or may not be inconsistent
• C)
• D)

\left( {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 0 \\\ 0 \\\ 0 \end{array}}&{\begin{array}{*{20}{c}} 0 \\\ 0 \\\ 0 \end{array}} \end{array}} \right) {\text{is an example of - - - - - - - matrix}}{\text{.}}

• A) Zero
• B) Non-Singular
• C) Singular
• D) Column

The equation 0x - 0y = 0 has __________ solution(s).

• A) Infinite many
• B) No
• C) multiple finite
• D) Unique

\[\begin{array}{*{20}{c}} {{\text{For the following system of Equations:}}} \\\ {x + 2y = 0,{\text{ }}2x - y = 0{\text{;}}} \\\ {{\text{the solution set is - - - - - }}{\text{.}}} \end{array}\]

• A) $${\text{Line through origin in}} ~{\mathbb{R}^3}$$
• B) $${\text{Any arbitrary line in}} ~{\mathbb{R}^2}$$
• C) $${\text{Line through origin in}} ~{\mathbb{R}^2}$$
• D) $${\text{Real line}}~ \mathbb{R}$$

The determinant of the matrix A is denoted by

• A) $\bar{A}$
• B) $A^T$
• C) $|A|$
• D) $A’$

Order of matrix is based on the numbers of _______.

• A) (b) elements
• B) (d) both (a) and (c)
• C) (c) columns
• D) (a) rows