$$\sin y + \sin x = 1,$$ is an example of __________ Equation.

• A) Linear
• B) Non - Linear
• C) Quadratic
• D) Homogeneous

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

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

A linear system is said to be _____ if it has no solutions.

• A) inconsistent
• B) consistent
• C)
• D)

A linear system is said to be ______ if it has at least one solution.

• A) consistent
• B) inconsistent
• C)
• D)

The variables in a linear system are called the _____.

• A) unknowns
• B) knowns
• C)
• D)

The homogeneous equation Ax = 0 has a nontrivial solution if and only if the equation has ___________

• A) at least one free variable
• B) at least two or more free variable
• C)
• D)

If $$\alpha = \beta ,$$ then $$\left| {\begin{array}{*{20}{c}} {\cos\alpha }&{ - \sin\alpha } \\ {\sin\beta }&{\cos\beta } \end{array}} \right|$$ =________.

• A) $$\cos 2 \alpha$$
• B) $$\infty$$
• C) $$\sin 2 \alpha$$
• D) 1

Basis is a spanning set that is as small as possible

• A) True
• B) False
• C)
• D)

How many Pivot positions the matrix $$\left( {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 2&3&1 \end{array}} \\ {\begin{array}{*{20}{c}} 4&6&2 \end{array}} \end{array}} \right)$$ will have?

• A) 1
• B) 2
• C) 4
• D) 3

$${\text{Which of the following system will have the trivial solution?}}$$

• A) $$x = y = 1$$
• B) $$x = 1, y = 0$$
• C) $$x = 0, y = 1$$
• D) $$x = y = 0$$

A finite set of linear equations is called a ____ system.

• A) linear
• B) nonlinear
• C)
• D)

Which of the following is an example of Matrix in Echelon form?

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

Two vectors are linearly dependent if and only if they lie________

• A) on the same line through origin
• B) on a line parallel to x-axis
• C)
• D)

$$\begin{gathered} {x_1} + 2{x_2} + 3{x_3} = 7 \hfill \\\\ 4{x_1} + {x_2} + 2{x_3} = 2 \hfill \\\\ - 4{x_1} + 3{x_2} + 9{x_3} = 4 \hfill \\\\\\ \end{gathered}$$ The augmented matrix for the system is -----------

• A) $\left[ {\begin{array}{*{20}{c}} 1&2&3 \\\\\\ { - 4}&1&2 \\\\\\ 4&3&9 \end{array}} \right]$
• B) $$\left( {\begin{array}{*{20}{c}} 1&2&3 \\\\\\ 4&1&2 \\\\\\ { - 4}&3&9 \end{array}} \right)$$
• C) $\left[ {\begin{array}{*{20}{c}} 1&2&3 \\\\\\ 4&1&2 \\\\\\ { - 4}&3&9 \end{array}\,\,\,\,\begin{array}{*{20}{c}} 7 \\\\\\ 2 \\\\\\ 4 \end{array}} \right]$
• D) $\left[ {\begin{array}{*{20}{c}} 1&2&3 \\\\\\ { - 4}&1&2 \\\\\\ 4&3&9 \end{array}\,\,\,\,\begin{array}{*{20}{c}} 7 \\\\\\ 2 \\\\\\ 4 \end{array}} \right]$

$${\text{Let A be the matrix of order 2}} \times {\text{3 and B be the matrix of order 3}} \times {\text{5,then which of the following is the order of the matrix AB?}}$$

• A) $$2 \times 5$$
• B) $$2 \times 3$$
• C) $$3 \times 5$$
• D) $$3 \times 3$$

$Let{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} T:{R^2} \to {R^2}{\kern 1pt} {\kern 1pt} {\kern 1pt} be{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} transformation{\kern 1pt} {\kern 1pt} {\kern 1pt} T({x_1},{x_2}) = (x,0).{\kern 1pt} {\kern 1pt} {\kern 1pt} The{\kern 1pt} {\kern 1pt} {\kern 1pt} null{\kern 1pt} {\kern 1pt} {\kern 1pt} space{\kern 1pt} {\kern 1pt} (or{\kern 1pt} {\kern 1pt} \ker nel)\,N(T)\,\,of\,T\,\,is$

• A) $(0,1)$
• B) $(0, x_2)$
• C) $(1, 0)$
• D) $(x_1,0)$

Which one of the following is a diagonal matrix?

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

We can add the matrices of ______________.

• A) different order
• B) same number of columns
• C) same number of rows.
• D) same order

$${\text{In }}{\mathbb{R}^2},{\text{Linearly dependent vectors lie on the same}} - - - - - .$$

• A) Line
• B) Plane
• C)
• D)

The determinant of a triangular matrix is the sum of the entries of the main diagonal.

• A) False
• B) True
• C)
• D)