MATH 131 Final: MATH 131 UMass Amherst Umass_FinalExam_2012
Document Summary
Spring 2005: 5 points use gaussian elimination to nd the inverse of following matrix. Indicate for each step which row operation you use. Thus, a is invertible for all values of k, except those for which 3k 2 + k + 30 = 0; that is, 3: 5 points find the matrix a of the linear transformation t : r2 r2 with. Spring 2005: 4 points sketch the image of the unit square under the linear transformation. 2: 6 points find the matrices of the following linear transformations: (a) t : r2 r2, a clockwise rotation of 30 , followed by a dilation by a factor of 5. A = 5 "cos( 30 ) sin( 30 ) cos( 30 ) # =" 5 3 sin( 30 ) 5 3 (b) t : r3 r3, the re ection in the x z-plane, followed by a dilation by a factor of 2.
