Question

Linear Algebra 1. One of the most important applications of linear algebra to electronics is to analyze electronic circuits that cannot be described using the rules for resistors in series or parallel such as the one shown figure in below. The goal is to calculate the current flowing in each branch of the circuit or to calculate the voltage at each node of the circuit. This circuit is called Loop Current Analysis of Electric Circuits. In this circuit and number of the loops are 3. 252 12 30 2 10V 2 55 13 502 Figure 1 la. Write a matrix R of size 3x3 for all resistances in the circuit 1b. Find Null(R), Row(R), Col(R), and Eig(R) 1c. Find Ba(Null(R)), Ba(Row(R),Ba(Col(R)), and Ba(Eig(R)) 1d. Calculate Dim(Null(R), Rank(Null(R), Nullity(Null(R)), Dim(Row(R) Rank(Row(R), Nullity(Row(R)), Dim(Col(R), Rank(Col(R), Nullity(Col(R) Dim(Eig(R), Rank(Eig(R)), Nullity(Eig(R) le. Is diaganalizable? If yes then diagonalize it