MATH 211 Midterm: MATH211-P09-LEC20-Old-Midterm-Exam
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Please write your name on the very last page. [marks: let a be the 3 4 matrix: 4 (a) find an invertible matrix u of size 3 3 such that the product u a = r is the reduced. 2. (a) use matrix inversion to nd x and y if (cid:26) 2x + 5y = 1. 3x + 4y = 2. (b) find t (cid:18)(cid:20) 1 and t (cid:18)(cid:20) 5. R2 is a linear transformation with t (cid:18)(cid:20) 2. [18: use row operations to nd the inverse of a = Page 5 of 7: let a = [6] (b) find the (2, 3)-entry of the inverse a 1 of a. [12: express the matrix a = (cid:20) 3 7. 1 2 (cid:21) as a product of elementary matrices. Page 7 of 7: let p = (cid:20) 3/5 1/3. 2/5 2/3 (cid:21) be the transition matrix of a markov chain that starts in state 1.
