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

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Math 205 A B Quiz 06 gold page 1 11/02/2012 Name. we jested Soluhions 1. Find the determinant of the following matrix by hand, showing all your steps (intermediate results) along the way. Make good use of 0’s. Circle your final answer. i: ‘| = (by 3"4cden) Offs] Ola owos 245 Pe 43 5 o1l-o/4 90 6 906 = 2 24s Nese |" ON dle ee (does gl som it) 2. Let B= | a b c |; suppose det(B)=5 rst Find the determinant of each of the following matrices, and under each matrix write the reason/rule/fact about determinants of matrices you used to find the det. (eg, “swapping rows changes the sign of the det” or “the determinant of the derivative of a matrix is the matrix of its integral” (this second fact is nonsense) 2a) wa [283] 2) v-| Be og |NJ=5 be 4 ct r+2 s+4 t+8 [m] = [8*| = lo|=5 WV is obturck fom B by bie He obats fm matric ancl "< Gres", Tn. ou ane trospne ce He sone. Clay fb vdelying ht 2) Qala be a -[? * © |g ode et be del fom i 124 from By elemandong (00% ult ng Od a ee ene bor fe .abtont 70 copie f cos 3 ede. of He ctatiy marx by - focerd we so_ ok (Q) = 70 dt (B)= SO ie ate =O, 2e) =9S=4B dit (s) = cht (48) ut Aer y oe(a)! 2 the: & becaae EACH cur of 8 guts melitid by 1, hance at (4B)= 4-4-4. oleb(e) 3) Suppose the following elementary row operations turn the matrix A into U: = Gx S2 320 First, rows ry and r2 are swapped. Second, rs — r3 + 10r2, Third, row 1 is multiplied by 4. The matrix U is a 3 x 3 upper triangular matrix, with main diagonal entries 4, 3, and 2. 3A) What is det(A)? Explain. Mepraex Hoos (On op by lamenting atris E, E. 2 Ey , rapehie, Wen Wl tt &4,6A =U. 9: dk (EE, EA) dt(U) ths — dlat (Ey) leh (64) deh (G) Lilt) = del) ate 3B) Is A invertible? Explain how you know. Ly = _ 24. Ae inverhble be (“a) () (-1)- /al 7 W 3 2\=>|A| ~4 Uk (4) O.