MATH-205 Midterm: Bates MATH 205 111813buell205examb
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Name: by writing my name i swear by the honor code. And b = : (4 pts) Find the eigenvalues of b: (5 pts) If so, nd p and d such that a = p dp 1: (5 pts) determine whether b is diagonalizable. Row(a: (9 points) given an m n matrix a. Prove (verify in generality) that nul(a) is a subspace of rn: (10 points) If a is a 2 2 matrix and has 2 distinct eigenvalues, then a must be diagonalizable. If matrices a and b have the same reduced row echelon form then row(a) = row(b). If h is a subspace of r3, then there is a 3 3 matrix a such that h = col(a). A linearly independent set in a subspace h is a basis for h: (8 points) consider vectors of the form, (3 pts) Show that the vectors form a subspace of r4. a 2b + 5c.
