Whenever a solution set is described explicitly with vectors, we say that the solution is in parametric vector form.The equation x=su+tv (s, t in R) is called a

• A) parametric vector equation of the line
• B) parametric vector equation of the plane*
• C)
• D)

The Equation $$2x - 3y + kz = 4$$ is linear in _________.

• A) $$x,y ~{\text{and}}~ z$$
• B) $${\text{any one variable}}$$
• C) $$x, y, z ~{\text{and}}~ k$$
• D) $$x ~{\text{and}}~ y ~{\text{only}}$$

Which of the following would be the Augmented Matrix associated with the system $$\begin{gathered} \begin{array}{*{20}{c}} {2x = 1} \\ { - 2y = x ?} \end{array} \\ \end{gathered}$$

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

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

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

The equation $Ax=b$ has a solution if and only if

• A) b is the linear combination of the columns of A
• B) b is a non-linear combination of the columns of A
• C)
• D)

$${\text{Slope and }}y{\text{ - intercept of }}y{\text{ - axis are - - - - respectively}}{\text{.}}$$

• A) $${\text{both undefined}}$$*
• B) $${\text{undefined and zero}}$$
• C) $${\text{both zeros}}$$
• D) $${\text{zero and undefined}}$$

$$\begin{gathered} {\text{Under which of the following condition, a system of Linear Equations whose }} \ {\text{Row - Reduce form is }}\left( {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 1 \\\ 0 \end{array}}&{\begin{array}{*{20}{c}} 2 \\\ 0 \end{array}}&{\begin{array}{*{20}{c}} | \\\ | \end{array}}&{\begin{array}{*{20}{c}} { - 1} \\\ {h - 3k} \end{array}} \end{array}} \right){\text{ has NO solution?}} \\\ \end{gathered}$$

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

$$\sin y + \sin x = 1,$$ 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)