\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

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

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

If the order of matrices A, B and C are 2*3, 3*15 and 15*100 respectively, then the order of Product ABC= -------.

• A) 2*100
• B) 200
• C) 405000
• D) 100*2

\eqalign{ & If A = {A^t} ( Where A is a square matrix), then which of the following \cr & is the most appropriate option for A \cr}

• A) A is singular matrix.
• B) A is a scalar matrix.
• C) A is symetric matrix.
• D) A is invertible matrix.

The matrix M = \left[ {\,\begin{array}{*{20}{c}} a&4&5&6\\\7&a&4&5\\\8&7&a&4\\\9&8&7&a \end{array}\,} \right] is a ______ matrix.

• A) Diagonal
• B) Toeplitz
• C) Identity
• D) Rectangular

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

Consider an LU-factorization, the matrix L is _____ and is called a unit lower triangular matrix.

• A) Singular
• B) Invertible
• C) zero
• D) Identity

Which of the following is true for the partitioned matrices Y = [\,Q\,\,\,\,\,\,\,\,R\,]\,\,\,{\rm{and}}\,\,\,Z = [\,U\,\,\,\,\,\,\,\,V\,]\,, where sub-matrices Q and R have the same sizes as U and V respectively?

• A) Y + Z = \left[ \begin{array}{l} \,QU\\\RV \end{array} \right]
• B) Y + Z = [\,QU\,\,\,\,\,\,\,RV\,]\,
• C) Y + Z = [\,Q + U\,\,\,\,\,\,\,R + V\,]\,
• D) Y + Z = \left[ \begin{array}{l} \,Q + U\\\R + V\, \end{array} \right]