MATH 546 Midterm: MATH546 South Carolina su01 4 nospace
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If needed, use the back or the next empty page for work. If you need additional paper, write your name on it: do not detach pages from this exam packet or un-staple the packet, please write neatly. Answers which are illegible for the grader can not be given credit: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. If a is a non-invertible n n matrix, then det(a) 6= det(rref(a)). A as well as rref(a) have determinant 0. If the rows of a square matrix form an orthonormal basis, then the columns must also form an orthonormal basis. You have proven that aat = 1n is equivalent to at a = 1n. A 3 3 matrix a for which the sum of the rst two columns is the third column has zero determinant. The matrix is not invertible in that case.
