MATH 1502 Midterm: MATH 1502 GT Practice Exam3 v1
Document Summary
Math 1502, practice problem set for exam 3: find the inverses of the following matrices if possible, find the determinants of the following matrices. 2 2 1 x x x x x 2x x x. 0 3(cid:21) (a) (cid:20)2 a (b) y z(cid:21) (a) (cid:20)x (b) (d) (c) 4: find, a basis of the null space, a basis of the column space, the rank of the following matrices: 2: find a basis and the dimension for the following subspaces: Satisfying the relation x + 2y + 3z = 0. Satisfying the relation x = 2y 3z and 4x + 5y + 6z = 0. 7 8 (a) span (b) vectors (c) vectors . 3 x y z x y z: show that b = (cid:26)(cid:20)1 (a) find the coordinates [x]b and [x]c (relative to the bases b and c, respectively) B to basis c: compute eigenvectors, corresponding eigenvectors (eigenspaces), and diagonalize the following matrices if possible.
