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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

( | cosΘ | sinΘ | )^{-1}= |

-sinΘ | cosΘ |

( cosΘ sinΘ ) -sinΘ cosΘ ( -cosΘ sinΘ ) sinΘ cosΘ ( cosΘ sinΘ ) sinΘ -cosΘ ( cosΘ -sinΘ ) ✔ sinΘ cosΘ

x

_{1}=0=x

_{2}

can be expressed in the form

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

( | 3 | 4 | )? |

1 | 2 |

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

- No
- Unique ✔
- Infinite many
- distinct multiple

- No ✔
- Unique
- Infinite many
- distinct finite

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

( | 1 | 2 | | | -1 | ) |

0 | 0 | h-3k |

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

x+2y = 0, 2x-y=0;

the solution set is ___

- Real line ℝ
- Line through origin in ℝ
^{2} - Line through origin in ℝ
^{3} - Any arbitrary line in ℝ
^{2}✔

{ | ( | 1 | ) | , | ( | 0 | ) | } is Linearly ___ in ℝ^{2} |

2 | 0 |

- Independent ✔
- Dependent

| | x | 2 | | = x | | 5 | -2 | |, is |

3 | -1 | 3 | -1 |

- -3 ✔
- 3
- 6
- -6

[ | 2e^{-3t} |
] = [ | 2 | ]? |

5e^{-3t} |
5 |

- ∓1/3
- 1
- 2/5
- zero ✔

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

( | -2 | ) and ( | -66 | ) |

3 | 99 |

- 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

- -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