-3 Let A = -4 -3 -1 9 Define the Lnead teanofamatia T:IR²> IR° by T2)= AR. Find the inages of ů= [oI and P= [6] undleR T. TCR) =

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The variables are independent.

Number 3b

Which of the tollawing diferential eouations corresponding to the potertial Vix) = 2x – x * - 3x +2 = 0 Oi+ 3x -2 = 0 - x + 2 = 0 x+x -2 =0

4: a) Let X. X,, X -N (Hi,6). Let Y,, Y2 Ym-N (2.63). nd (1-a) % CI for oi/ when ui. a known b) Let X, X2, ..X-f(x) 3D Sex-(@+1) x > 1 find Suff. Comp. St. e. w.

D Consi der He ,follwing - {(01), (-1)}, 8'- {12,0), (4.4)}, B= %3D O Find the froms fiom mabria from B to B. ® Find the trami tion mabis from B' to B © Vevify that the two tramsition mapices ínverves of earh other. %3D O Find the coofinate mafix [x Je, gimn ceo dinate mafix [«]g. the

Show that zxx + Zyy O from the equation z = In(x² + y²) %3D

Find the valueof the consraut (min) that makes the DaE f X dx -Cyf~*) dy so CHomogeneous, exect, separable aud Linear)

How, Form p.D.E. from a (3) Ucx, y) = (x²+a)lytb)