Problem 5. This problem is to familiarize yourself to tensor product of vector spaces. Consider the space (C2 (X) (C2 recall that if we denote the basis for (C2 by {|O) , |1)} (as is customary in the quantum information notation), (C2 @132 is a space spanned by {|0, O) , |0, 1) , |1, 0) , |1, 1)}. We can the identify C2 C2 g (C4 by mapping |0,0) > |1) , |0, 1) ) |2) , |1,0) > |3) , |1, 1) > |4). (a) Write down an expression for an ()0 [,1] [ml ' as a vector in (C4. Similarly, write down an expression for the tensor product of two 2 X 2 matrices 100 101 (8) boo b01 am 0511 510 (711 ' (b) Verify by explicit computation that, for a, b E C2 and A, B E C2\