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Systems of Linear Equations

Problem 1:

1. Enter the following three matrices:

Check the following linear algebra rules:

• Compute A + B and B + A. Is matrix addition commutative?
• Compute AB and BA. Is matrix multiplication commutative?
• Compute (AB)C and A(BC). Is matrix multiplication associative?

Problem 2:

Using Matlab, find the solution x, y, z to the system of equations:

Problem 3:

For the circuits given below:

• Write down all equations you obtain from KCL, KVL, and Ohm’s law.
• Set up a system of linear equations to calculate all voltages in the circuit.
• Using Matlab, solve the systems of linear equations.
• Determine all currents given in the circuits.