MATH-205 Midterm: Bates MATH 205 030504ross205exam
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Initials: let a be the matrix below. Recall that the null space of a is the set of solutions of the equation ax = 0. Recall also that the column space of a consists of the vectors b for which the equation ax = b has at least one solution. I"d row reduce the matrix [a|b1|b2] all at once, rather than use two separate augmented matrices. Find all the vectors in the null space of a, writing them in terms of a linear combi- nation of appropriate column vectors using free variables. Initials: let a be the following matrix. Find an lu factorization of a by the method we have used in class. Do not multiply rows by scalars or swap rows in nding u ; only add/subtract multiples of one row to/from another. Initials: suppose a is a matrix whose lu factorization is. Use the lu factorization of a to solve the equation ax = .
