Subset - Linear Algebra - Solved Exam, Exams of Linear Algebra

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MATH 205 EXAM 2 MArcH 20, 2008 NAME: Re YOUR GRADE IS BASED ON CORRECTNESS, COMPLETENESS, AND CLARITY ON EACH EXERCISE. YOU MAY USE A CALCULATOR, BUT NO NOTES, BOOKS, OR OTHER STUDENTS. Goop Luck! 1.) (15 pts.) a.) (10 pts.) Consider the subset of P, of all polynomials of the form p(t) = a+ bt”, where ais in R and 6 is in R. Demonstrate that this subset is a subspace of Po. ) Let PWD= arb with aad bh inh, at Els crdtt, ott, . Card d inl. Tren (Fea ER) = (area) +lcedt®) = Cate) Hlo4at®, wie arc ia Toad bid ia MR. Therefare Ga » la Hae set. with a ad bin Ry ad che «a rel soles, 2 L 2) Ler f bd roe © : sca eeptt sith ca ow ch in R, own (eye claebe awesetore CoP) id ia Hoe sete 3) the wm vector is ja the Set. To See this, deb aabeo. These are the Aaeee Yring ust needed to verify do show the ser bo % subspace. b.) (5 pts.) Let H be the set of points inside and on a circle of radius 2 that is centered at the origin of the cy—plane. That is, H = {(z,y): a? +y? < 4}. Use an example (two vectors, or a vector and a scalar) to show that H is not a subspace of IR*. He [t) is ta He Hosen, fr the mop ca le ia aah ia BH. Stpdas S , Sy > 3° pot closed unde Scolar aad His pst a fubsgace Anil mtn? roU mud fiction, hich ms ot Rm.