1. For the matrix A below, nd a basis for ColA and NuIIA, and determine their dimensions. 1 2 9 5 4 1 1 6 5 3 2 0 6 1 2 4 1 9 1 9 2. Consider the following vectors in R2: m l 1 br[ l ands-:1- Suppose that a subspace H has basis .93={b1, b2] Find the 93- coordinate vector of x. 3. Let A, B be the matrices below. These are called the Pauli spin matrices used in the study of electron spin in quantum mechanics. Show that A2 = 1,32 = I, and that AB = BA. Matrices such that A B = BA are said to anti-commute. _l 0 _ 01 A[O _1]andB[10] 4. What are the possible ranks of the matrix M below, and Why? 5 7 M = ls l 5. For n = 0,1,2,3, construct an example of a 3 X 3 matrix of rank n, and justify your