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
- 1
- 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
- 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
- No
- Unique
- Infinite many ✔
- multiple finite
