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By D.O. Shklyarsky, N. N. Chentsov, I. M. Yaglom, V. M. Volosov, I. G. Volsova

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I ~:~J l i n your software, set the di splay forma t to show as many decimal places as possible. then compute Compu te 8 r C and mult iply the result by A on the ri ght. (Hi",: B TC is I x I ). (c) 4 1. Let A 8 = IO . A. Explai n why ( A8 T )C = ( 8 T C) A . C - A + A + A + A + A + A + A + A+A+A. 3 1. Determin e a constant k such thaI (k A )T (k A ) = I, where ~ [~:l '''h,re m""h,"o~ "'000" 'h" oo,'d and A D = 8 - C. be used? If D is not O. :omputin g enllironment. (It is nOl unu sual that D 0, since many computing enllironment s use onl y II "model" of exac t arithmetic, called floatin g-po illl :lrithmeti c,) 32, Find three 2 x 2 matri ces.

Show that (A _ 8 )T = A T _ 8 T. 36. Le t X I and X2 be solutions 10 tl:e homogeneous linear system Ax = O. (a ) Show that XI + X1 is a sol ution. (b) Show that XI - X2 is a solu tion. 42. Let A = [: : ] . In you r software, set the display to show as llIany decimnl places as possible. Expe riment to find a posith'c intege r k such that A + IO-t • A is equal to A. If you find su: h an intege r k. you ha\'c lIerified that there is more than onc matrix in your com putational enll ironment that pla)s the role of O .

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Selected Problems and Theorems in Elementary Mathematics by D.O. Shklyarsky, N. N. Chentsov, I. M. Yaglom, V. M. Volosov, I. G. Volsova


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