Quantum Computing gate matricies

[Fixxxer125]

Hi there
I am working through a quantum gate section of my course and I am a bit puzzled on how to calculate a matrix for consecutive quantum gates. I understand how to generate a matrix for

|q₀⟩--------[H]-------
|q₁⟩------------------
Which is simply the tensor product of the hadamard and identity matrix. However I am unsure what to do if the circuit is modified to be have a CNOT gate after the hadamard gate with the top qubit as the control and the bottom as a target. i have tried adding the matricies but this doesn't seem to work. Thanks for your time

 

[Wolfgang2b]

You should do matrix multiplication(keeping in mind the order) not addition.

The matrices represent operations (hence operators) done on the state. So if we take the input state as |in>, have state after the above circuit is (H x I)|in>, which is then the input to CNOT gate. So finally you get |out>=CNOT((H x I)|in>) which is equivalent to matrix multiplication of CNOT with H x I and |in>

 

[Fixxxer125]

Thanks for your help!