MTH501 Quiz 1 Set 3

Q1. $${\text{In }}{\mathbb{R}^2},{\text{Linearly dependent vectors lie on the same}} - - - - - .$$

1. Plane
2. Line

Correct answer: Line

Q2. $Let{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} T:{R^2} \to {R^2}{\kern 1pt} {\kern 1pt} {\kern 1pt} be{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} transformation{\kern 1pt} {\kern 1pt} {\kern 1pt} T({x_1},{x_2}) = (x,0).{\kern 1pt} {\kern 1pt} {\kern 1pt} The{\kern 1pt} {\kern 1pt} {\kern 1pt} null{\kern 1pt} {\kern 1pt} {\kern 1pt} space{\kern 1pt} {\kern 1pt} (or{\kern 1pt} {\kern 1pt} \ker nel)\,N(T)\,\,of\,T\,\,is$

1. $(0,1)$
2. $(x_1,0)$
3. $(0, x_2)$
4. $(1, 0)$

Correct answer: $(0, x_2)$

Q3. We can add the matrices of ______________.

1. same number of columns
2. same number of rows.
3. same order
4. different order

Correct answer: same order

Q4. $${\text{Which of the following system will have the trivial solution?}}$$

1. $$x = y = 0$$
2. $$x = 0, y = 1$$
3. $$x = y = 1$$
4. $$x = 1, y = 0$$

Correct answer: $$x = y = 0$$

Q5.

1. $${B^t}{A^t}$$
2. BA

Correct answer: $${B^t}{A^t}$$

Q6. Two vectors are linearly dependent if and only if they lie________

1. on a line parallel to x-axis
2. on the same line through origin

Correct answer: on the same line through origin

Q7. $$\begin{gathered} {\text{What will be the order of matrix:}} A - B{\text{, if the orders of both}} ~ \ A ~{\text{and}} ~B ~{\text{is}}~ 2 \times 3? \\ \end{gathered}$$

1. $$2 3$$
2. $$0 0$$
3. $$2 2$$
4. $$3 3$$

Correct answer: $$2 3$$

Q8. A system of linear equations is said to be homogeneous if it can be written in the form ______________.

1. AX = 0
2. AX = B

Correct answer: AX = 0

Q9. $$\begin{array}{*{20}{c}} {{\text{The system of equations}}:} \\ {{x_1} = 1, } \\ \begin{gathered} {x_2} = 0; \ {\text{can be expressed in the form - - - - - }}. \\ \end{gathered} \end{array}$$

1. $${array}{*{20}{c}} {Ax = 0} \\ {By = 1} {array}$$
2. $${array}{*{20}{c}} {Ax = 1} \\ {By = 0} {array}$$
3. $$Ax = 0$$
4. $$Ax = b$$

Correct answer: $$Ax = b$$

Q10. Linear algebra is the study of linear sets of equations and their ---------------- properties.

1. transformation
2. non-linear

Correct answer: transformation