# Solution Library

# Create a Matrix From Linear Equations and Determine Current Using MATLAB

**Question**

a) An analysis of an electrical resistor circuit with two dc voltage sources *E1 *and *E2 *produces following equations from which the loop currents *i1,i2 and i3 *are determined:

(*R*1 + *R*2 + *R*3)*i*1 - *R*2*i*2 - *R*3*i*3 = -*E*1

-*R*2*i*1 + (*R*2 + *R*4 + *R*5)*i*2 - *R*5*i*3 = 0

-*R*3*i*1 - *R*5*i*2 + (*R*3 + *R*5 + *R*6)*i*3 = *E*2

Let *R*1 = *R*3 = *R*5 = 1 ohm, *R*2 = *R*4 = *R*6 = 2 ohm, E1= 2V and E2=3V, Display the matrices formed using the above equations and determine the loop currents *i1,i2 and i3 *

b) For each of the following set of linear equations, find x and y. Also comment on the existence and uniqueness of the solution (i.e no / unique / infinite solutions) by finding out required ranks and comparing it with number of unknowns. If it has a unique solution, find the determinant and inverse of A.

(A is the coefficient matrix in AX=B).

i) x + y = 6 ; −3x + y = 2

ii) -6x + 2y = 2 ; −3x + y = 2

c) Rewrite the equations given in (b) as equations of straight lines. Find the point of intersection (x and y co-ordinates of the point where the lines intersect) and plot the lines. Compare your findings from (c) with your results from (b) with respect to existence and uniqueness.

**Summary**

This question belongs to MATLAB software and discusses about application of MATLAB in physics to solve linear equations and to determine current and voltage in a given circuit.

**Answer is in MATLAB format**

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