1. The nontrivial solution of the system of differential equation exist only when
 det(XλI)=0
 det(AλI)≠0
 det(A+λI)=0
 det(AλI)=0 ✔
2. Vectors
(  1  ) and (  2  ) are linearly ___ 
0  0 
 Dependent ✔
 Independent
3.
[  b_{11}  ] is a 
b_{21} 
 Row matrix
 column matrix ✔
4. Vectors
(  2  ) and (  66  ) are linearly ___ 
3  99 
 Dependent ✔
 Independent
5. Matrix form of the following system of nonhomogenous differential equations is
dy/dx = 2x +4y + e^{t} 4t
dy/dx = 3x4y+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?
 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 nonhomogenous 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 ✔