MTH 141 Midterm: MTH141 – F2007 Midterm1 (Solution)
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Part a: short answer: (2+8+4) consider the following system of equations x1 + 2x2 x3 + 3x4 = 1. + x2 + 2x3 + x4 = 1. 2x1 + 4x2 x3 + 4x4 = 2. + x4 = 1 x1 + 2x2 + (a) write down the augmented matrix of the system. 1 2 (b) use the row operations to nd the reduced row echelon form of the augmented matrix. 0 0 0 (c) write down all (if any) solutions to the above equations. x1 = 1 + 9t, x2 = 1 5t, x3 = 2t, x4 = t: (6+6+3) let a = (a) find a 1. 1 (b) find det(a). (c) solve ax = b. 2: (10) for the following matrices calculate the quantities below where possilbe. 1 # c = " 1 0 1. 2 4 # (a) at a b = " (b) abc = .
