MAT-2240 Final: MATH 2240 App State summer2006 Final Exam
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Use the backs of the exam pages for scratchwork or for continuation of your answers, if necessary. 200: (17pts): determine if the following system is consistent: x1. + 2x4 + 3x5 = 7 x4 + x5 = 3. If the system is inconsistent, nd an approximate solution which minimizes the error sum of squares : (17pts): determine if the following system is consistent: x1 + 2x2 + 3x3 = If this system is consistent, write the general solution in parametric form. If the system is inconsistent, nd an approximate solution which minimizes the error sum of squares : (20pts): let a = . Let w = null(a). (a) find a basis for w . Also, nd rank(a) and nullity(a). (b) show that s = If p is a re ection matrix, nd its line of re ection. If p is a rotation matrix, nd its angle of rotation: (20pts): let w = span.