Quadratic Form - Linear Algebra - Solved Exam, Exams of Linear Algebra

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MATH 205 FINAL EXAM APRIL 10, 2007 NAME: re (gas sre ose YOUR GRADE IS BASED ON CORRECTNESS, COMPLETENESS, AND CLARITY ON EACH EXERCISE. YOU MAY USE A CALCULATOR AND THE AGREED-UPON PAGE OF NOTES, BUT NO BOOKS OR OTHER STUDENTS. GoOopD Luck! 1.) (10 pts.) Given the quadratic form 8x? + 62,2, a.) (2 pts.) find the symmetric matrix of the quadratic form; ha b.) (2 pts.) classify the quadratic form as positive definite, negative definite, or indefinite, and explain your reasoning; ei a ~ = = A+] ) =o jana) = GEA) = AU a= oh 4) whee Az WH 4 so inde Laity (tigtnvaduer D ona ©) c.) (6 pts.) make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. : il = eee i _ hts oft eh an ant =‘ i). Go tere ee eye s \ >| >) or ) b Ey ele el ae "le 3 ~ | Ms te Ne oe ~\ . > bt 5 AEP eh eee G 15 Yuen Q uodratit Soran: wou NE toordinak S a oe