MATH 3406 Midterm: MATH 3406 GT Exam 2 Practice problems
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3. (a) give a de nition of the determinant. (b) use your de nition to prove that the determinant is invariant under type i and type. Ii elementary row operations: compute the determinant of the matrix. A = a1 a2 a3 a4 a5 b5 b2 b1. 5. (a) find the projection matrix p onto the column space of a, where. 0 3 (b) find a pseudo-inverse of a: let x and y be orthogonal vectors in a vector space v . 7. (a) find a basis for r2 m2 2. (b) show that m2 2 = w1l w2, where w1 = (cid:18) a b. B a(cid:19) and w2 = (cid:18)c d c(cid:19). d.
