Prelim 1Math 294Spring 2004no calculatorsanswer + reason = creditcondensed printout—there were 5 pages1.a)(17 points)Find the numberafor which the systemx1+ 3x3-x4= 20x1+ 2x2+ 2x4=ax1+ 4x2-3x3+ 5x4= 60has solutions, and find all solution vectorsx.b)(3 points)Give a definition: “u1,u2, . . . ,unare linearly independent iff —-”.2.(20 points)Find the inverseC-1ifC=1000210003100041.3.a)(8 points)Find a basis for the kernel ofD, ifDis the 5 by 5 matrix having a 1 in every position.b)(8 points)In this part, letv1=-1-111,v2=-111-1,e1=1000,e2=0100,e3=0010, ande4=0001. Find a basis forR4consisting ofv1andv2together with some of theek.c)(4 points)Give at least 4 examples of vectors in the image, imA, where
This is the end of the preview.
access the rest of the document.