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# MTH401-Differential Equations Quiz MCQs Lecture 23-45 Finalterm Objective Questions

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 ✔

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