Quantum gates transform a quantum state, and the underlying math is linear algeb

Quantum gates
transform a quantum state, and the underlying math is linear algebra. For this homework, you will
be writing matrix math expressions and showing your work by evaluating them.
Question 1 Design a 2-qubit quantum gate ? that performs an ? gate on the first qubit and a ? gate
on the second qubit.
Write the matrix expression for ? using ? and ?.
Write the matrix representations of ? and ?.
Evaluate your matrix expression and show the matrix representation for ?.
Can ? produce entanglement between the qubits it operates on? Yes | No
Question 2 Design a single-qubit quantum gate ? that performs an ? gate then a ? gate.
Write the matrix expression for ? using ? and ?.
Write the matrix representations of ? and ?.
Evaluate your matrix expression and show the matrix representation for ?.