ma232_exam3_soln - 7 1 Perform Gauss-Jordan elimination on the following matrix I am grading your work not just your answer so be clear what you are

ma232_exam3_soln - 7 1 Perform Gauss-Jordan elimination on...

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7 1. Perform Gauss-Jordan elimination on the following matrix. I am grading yourwork not just your answer so be clear what you are doing and write (20 pts) legibly. O -t ) il o r v+ o I - 2. Find the values of r and y that satisfy the following matrix equation. (10 pts) bJ 2 I O
3. Use the following linear first order differential equation to answer the a'+|a:# ; s(1):g(a) solve the initial value problem using integrating factors. ftr\ = F trt) = ir(x)Q('r\= C^fl'- ^!**\ - x$= 5 *{,},X3= lnlr-z) U'= *t,rl*-z)+ i3= irnl'-tl ?g':gt -au,\*rra br= f -f, = ?Cta-l)e)U= *4v,[x-.1 + ceToh ( o,z)4. Find and classify the equilibrium values of the autonomous differential (b) Give the interval where the solution from part (a) is unique. as stable or unstable.(10 questions. (1b pts) | x = J Q'r\f'1-t\ b=ot-l ,l1',S=lt=o3= -lr'1,l+ ^tJ qns+-he-l-\"I* I srl'bh--t1- 5r'tncl*bLUrt6la,tat{-SX*b\Lllagk'btc- s *- +C - O ** equation (b pts) pts) =o I
5. A linear system of equations in variab\es r,y, and z is given by the matrix ^li):lllwhere A is a 3 x 3 matrix. Suppose that the rref of the augmented follows:tlSuppose that z: 4 and find the values of r and y. [: ?]'l[ I,l;l ?, *,1 ";:::o f 1o tltlal o] - '1,Lo o 6. Find the general solution to the following first order differential equation. (12 equation matrix is as (12 pts) l.,, o | o 1 o pts) a':2xe-az4 xr't/s=o\- z 3 = ,(n[r'tc\x=-{6u= 7-),"; = z*e-1\so \ = \.* )'ue\ s X'+C =Q sn
F.,. ' :i?i*- ir'-i:.:3q-F6 7. Are the following in rref , ref , or (4 pts each) neither. 11 1 0-1.l(") lo o 1 Loooolef ,/neitber 1l (b) l; ; 3 ?]@"r/neitber(")(d)11 2-L Lr Btl,r"[email protected]liril,r"€"ileitber 11

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