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.
- Row matrix
- column matrix ✔
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 |
]et + [ |
-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 |
]et + [ |
-4 |
]t |
3 |
-4 |
y |
0 |
11 |
- X' = -2x + 4y + et - 4t, X' = 3x - 4y + 11t ✔