MTH401-Differential Equations Quiz MCQS #Objective #Questions #FinalTerm

1. The non-trivial solution of the system of differential equation exist only when

- det(X-λI)=0
- det(A-λI)≠0
- det(A+λI)=0
- det(A-λI)=0

2. Vectors

( |
-1 |
) and ( |
2 |
) are linearly ___ |

0 |
0 |

3.

4. Vectors

( |
-2 |
) and ( |
-66 |
) are linearly ___ |

3 |
99 |

5. Matrix form of the following system of non-homogenous differential equations is

dy/dx = -2x +4y + e

^{t} -4t

dy/dx = 3x-4y+11t

X' = [ |
-2 |
4 |
] [ |
x |
] + [ |
1 |
]e^{t} + [ |
-4 |
]t |

3 |
-4 |
y |
0 |
11 |

6. If A is a m X n matrix and A=A

^{T} which of the following must always be true?

7. A matrix is defined as

A = [ |
a |
b |
], k is a constant then |

c |
d |

- A = kA
- Ak = kA
- -Ak = Ak
- Ak ≠ kA

8. If

is an eigenvector of the given matrix

A = [ |
1 |
0 |
] then AK is |

0 |
1 |

9. Let

A = [ |
a |
b |
] and B = [ |
u |
v |
] then A + B is |

c |
d |
x |
y |

A + B = [ |
a + u |
b + v |
] |

c + x |
d + y |

10. The equation form of a non-homogenous system of differential equations

X' = [ |
-2 |
4 |
] [ |
x |
] + [ |
1 |
]e^{t} + [ |
-4 |
]t |

3 |
-4 |
y |
0 |
11 |

- X' = -2x + 4y + e
^{t} - 4t, X' = 3x - 4y + 11t