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 |
- Dependent ✔
- Independent
3.
| [ | b11 | ] is a |
| b21 |
- Row matrix
- column matrix ✔
4. Vectors
| ( | -2 | ) and ( | -66 | ) are linearly ___ |
| 3 | 99 |
- Dependent ✔
- Independent
5. Matrix form of the following system of non-homogenous differential equations is
dy/dx = -2x +4y + et -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=AT which of the following must always be true?
- m ≠ n
- m = n ✔
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
| K = [ | 1 | ] |
| -1 |
is an eigenvector of the given matrix
| A = [ | 1 | 0 | ] then AK is |
| 0 | 1 |
- 1K ✔
- -1K
- 1
- -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 ✔
