Practice Test: Practice Midterm #2 (Version B)

Please provide details and problems thoroughly worked through. Will use as a study guide for exam, exam will present VERY similar questions. Thank You.

Problem 1. 2.1 Matrix Operations Given the matrices A, D and C below, compute the requested: 111 600 52 A=123,D=020,c= 1 0 145 003 35 (a) A 213, 213A (b) AD, DA, AC, and CD Problem 2. 2.2 Inverse of a Matrix Find the inverse of the following matrices: M [i 3i [3 ii 1 o 3 (b) 4 1 4 2 2 4 Problem 3. 2.3 Characterizations of Invertible Matrices Determine if the following matrices are invertible. Show the rational. (a) CO N ( b ) NIN OHH HOO Problem 4. 2.4 Partitioned Matrices Find X, Y and Z in terms of A, B and C for the following partitioned matrices. Assume they are partitioned conformably for block multiplication. (a) [ ] [ x ] = [2 0] Problem 5. 2.5 Matrix Factorizations Find an LU factorization of the following matrix. UINK 10Problem 6. 3.1 Introduction to Determinants Compute the determinant of the following matrix using cofactor expansion. Problem 7. 3.2 Properties of Determinants Combine the methods of row reduction and cofactor expansion to compute the determinant of the following matrix. 3 4 3 1 3 0 1 3 6 0 4 3 6 8 4 1 Problem 8 3.3 Cramer's Rule Use Cramer's rule to compute the solution of the system below (two points). Compute A '1 for an additional two points extra credit. X1 + JCZ = 3 3X1 + 2.963 = 0 x2 2.X3=2