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

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 + 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?

• 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 + e^t - 4t,     X' = 3x - 4y + 11t ✔