# Complexity Explorer Santa Fe Institute ## Vector and Matrix Algebra

• Introduction to this Tutorial
• Sets and Set Notation
• Proof of the Infinitude of Primes
• Boolean Set Operations
• Vectors and Vector Operations
• Matrices
• Matrix Operations
• Essential Types of Matrices
• Vector Spaces
• Determinants
• Eigenvalues and Eigenvectors
• Diagonalization and Powers
• Geometric Transformations
• Differentiation as a Matrix Operation
• Markov Chains

#### 1.4 Boolean Set Operations » Quiz #3 Solution

Question 1: The union of A and B is equal to A, since the elements of B (4 and 5) are already in A.  The complement of A (with respect to universe U) is {8, 9, 10}.

Question 2: Recall that the Cartesian product is a set whose elements consist of all possible two-component pairs from the two sets (here, B and B).   Since B = {4, 5}, we get the set of all possible 2-element pairs using those elements.

Question 3: The elements of are three-component vectors created by taking each element of A for the first component, and for each of those taking each element of B for the second component, and then for each of those, taking each element of U for the third component.  There are 7 possible first components (values from A), times 2 possible second components (values from B), timex 10 possible third components (values from U).  7 times 2 times 10 = 140.