MTH501-Linear Algebra Quiz MCQs Lecture 1-22 Midterm Objective Questions | SUPERSTARWEBTECH

MTH501-Linear Algebra Quiz  MCQS #Objective #Questions #Midterm

1. Which of the following system will have a trivial solution?

• x = y = 1
• x = 1, y = 0
• x = 0, y = 1 ✔
• x = y = 0

2.

 ( cosΘ sinΘ )-1= -sinΘ cosΘ
•  ( cosΘ sinΘ ) -sinΘ cosΘ
•  ( -cosΘ sinΘ ) sinΘ cosΘ
•  ( cosΘ sinΘ ) sinΘ -cosΘ
•  ( cosΘ -sinΘ ) ✔ sinΘ cosΘ

3. The system of equations:
x1=0=x2
can be expressed in the form

• Ax=0 ✔
• Ax=b
• Ax=0, By=1
• Ax=1, By=0

4. Which of the following is Row – Equivalent of

 ( 3 4 )? 1 2

•  ( 2 -4 ) -1 3
•  ( 3 1 ) 4 2
•  ( 4 3 ) 2 1
•  ( 1 2 ) ✔ 3 4

5. The system of equations : y=0 and x=5 has ___ solution(s).

• No
• Unique ✔
• Infinite many
• distinct multiple

6. The equation : 0x-0y=-5 has ___ solution(s)

• No ✔
• Unique
• Infinite many
• distinct finite

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

•  ( 0 1 ) 1 0
•  ( 0 0 ) 1 1
•  ( 1 0 ) ✔ 0 1
•  ( 0 1 ) 0 1

8. Under which of the following condition, a system of Linear Equations whose Row-Reduce form is

 ( 1 2 | -1 ) 0 0 h-3k

has Infinite many solutions?

• h=3k ✔
• h ≠ 3k
• (h,k) = (0,0)
• (h,k) ≠(0,0)

9. For the following system of Equation:
x+2y = 0, 2x-y=0;
the solution set is ___

• Real line ℝ
• Line through origin in ℝ2
• Line through origin in ℝ3
• Any arbitrary line in ℝ2

10.Set

 { ( 1 ) , ( 0 ) } is Linearly ___ in ℝ2 2 0

• Independent ✔
• Dependent

11. The value of x satisfying the equation:

 | x 2 | = x | 5 -2 |, is 3 -1 3 -1
• -3 ✔
• 3
• 6
• -6

12. Which of the following would be the value of t, if

 [ 2e-3t ] = [ 2 ]? 5e-3t 5
• ∓1/3
• 2/5
• zero ✔

13. Which of the following corresponding Matrix form of the Linear equation x+y=3?

•  x ( 1 ) + y ( 0 ) = 3 ( 1 ) 0 1 0
•  x ( 1 ) + y ( 0 ) = 3 ( 0 ) 0 1 1
• x |1| + y |1| = 3 |1| ✔
• can’t be expressed in Matrix form

14. Vectors

 ( -2 ) and ( -66 ) 3 99

are linearly?

• Dependent ✔
• Independent
15. Which of the following is true about the existence of free variables (parameter) in a system of Linear Equations?
• They guarantee the Consistency ✔
• They guarantee the inconsistency
• They do not guarantee the consistency
• None

16. Slope and y-intercept of the line: 2x+3y=-1 ___ respectively

• -2/3 and -1/3 ✔
• 2/3 and -1/3
• -2/3 and 1/3
• 2/3 and 1/3
17. The equation 0x-0y=0 has ___ solution(s).
• No
• Unique
• Infinite many ✔
• multiple finite