# Linear Systems

This set of MATLAB Multiple Choice Questions & Answers (MCQs) focuses on “Linear Systems”.

1. What is a linear system?
a) A system which follows homogeneity and additivity
b) A system which follows additivity
c) A system which follows homogeneity
d) Almost every system is linear

2. What is the output if the following code?

```if(eig(A)==eig(A’))
disp(‘True’)```

a) True
b) No output
c) False
d) Error

3. A student has to find a solution for a system of equations having three variables. He has defined the coefficient matrix as C while the variable matrix as d. He observes that the system is homogeneous. So, to find the solution, he must first check
a) Consistency
b) Homogeneity
c) Heterogeneity
d) Linearity

4. The command to find the eigen vector of a matrix in matrix form is _____________
a) eig(a,matrix)
b) eig(a,’matrix’)
c) eigen(a,matr)
d) eig(a)

5. The nature of the eigen matrix displayed in MATLAB is ___________
a) Unsorted
b) Sorted
c) Sorted in Ascending order
d) Sorted in Descending order

6. Checking the linearity of a system, the first thing we need to check is whether the system is __________
a) Homogeneous or not
b) Consistent or not
c) Superposition
d) Depends on the representation of the system

7. In MATLAB, how can we check linearity of systems represented by transfer function?
a) Check waveforms after superpostion
b) Compare rank of matrices
c) Go for Rouche’s Theorem
d) Intuition

8. How can we check in MATLAB if an electrical circuit is linear or not?
a) Check consistency
b) Superposition
d) Check homogeneity

9. How can we find the solution of a nonhomogeneous system of equations without dealing with the rank of matrices?
a) Rouche’s theorem
b) Cramer’s rule
c) Gauss’s law
d) Cannot be done

10. For a homogeneous system, Cramer’s rule will always yield a trivial solution in MATLAB.
a) True
b) False

11. To apply Cramer’s rule, the condition is _________
a) Non-homogeneous system of equations
b) Homogeneous system of equations
c) Determinant of co-efficient matrix is not equal to 0
d) No condition

12. To apply superposition in MATLAB, the condition, one of the condition is ___________
a) No active element is present except sources
b) No passive element is present
c) System should have unilateral elements
d) Nothing needs to be checked

13. A second order system with no initial condition is always linear.
a) True
b) False

14. To check the rank of a non-singular square matrix, we have to use ___________
a) not required
b) rankm()
c) rankmatr()
d) rank()

15. A student aims to use Cramer’s rule to find a solution for a homogeneous system. But while finding the solution, he observes that he is getting infinity as a solution. The code is

`p=X.\C`

X is the matrix created by replacing a column with constant co-efficients in the equation.
C is the co-efficient matrix
P is one of the variables in the system
Is this a proper justification?
a) Yes
b) No
c) Maybe
d) It is not possible to find solutions in MATLAB