Calculations - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 205B Quiz 05 page 1 02/26/2010 Name. spy solhon 17 33 w zt 1. Let A=| 4 y and B=| > 7p Suppose that AB| r 56 |. 23 Bom s t 1A) Find ¢; skow the calculations. fe ‘ged rug A x 2 colin J 8" = 2S t2e (O42 = (2) 1B) Find y; show the calculations. W494 56> 4362 9) 1C) Find both w and x and again the work done to find them. Bw +2x = 12 A. cep [3 ae af ls) 4 [Srkow a 4 a orp? 2, Let A= [ ™ | ( 2A) In terms of m, k, g and h, what is A-!? maby nile mh-gh £O. mh “9k 4 ml »/ yy 2B) Suppose in fact that A= [ 4 e | Find all possible pairs of integers (k,g) for which A is not invertible. * Le need integer: 9 2K fe whel mh- gk = (5736) -gh = B-gh=0 such pars (ak) ax (18) (2 abo (es) 4-18) (-l9,4) ste a=[! eile al (29) hous a (4-3) 3,6) 43) (-3, 3A) Find the RREF of A “by hand”, one row operation Ge a time, and indicate! ‘your row ising our usual notation. bis [Fs] ESE SEL. AS 7] He KEP. thé oll a 3B) What are the elementary matrices corresponding to those row operations? Number them E, Ep, etc, in the order rou created them. s E (oma é [oO i | “| le ~ | 0 fo & Silo 3C) What product of the elems Cn fren step to step y matrices yields A~1? 3D) What product involvine of the elementary matrices equals A itself? Gree EG = =A, Gecyeayea