Number of Entries - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 205A Quiz 04 page 1 October 13, 2008 NAME Sutgestord solution 3 7 w 2 1.LeteC=]9 5 1 3] ltD= 2 0246 01 Find each of the following values. If the value doesn’t exist write “DNE” in the box, and give the reason. 3 5 7 . Suppose the 1-1 entry of the product CD is 51. i a. The number of entries in CD. G6 b. The 2-1 entry of CD. 77 “ . (Sige g (Bxt) (42) => 3x2. 5) FQtFl el2t30= 72454200 c. The 4-3 entry of CD. Nel d. The value of w. | /o ONE sine CO © 3x2 3-8t2lew2 20-51 2w = Si-24-7 = 20 e. The 3-2 entry of CT. 1 f. The 2-3 entry of (DC)™ DNE| 6 Ke 2-3 erty JC The plat OL vnllfied, 0, pe F g. The 2-3 entry of (CD)" HG h. The size of the matrix product CCT. AX oh 3-2 Gntn, pO: 03 +2:5+4.0+ 6+//=)b (3%) 4 (42) i. The 2-1 entry of DT D. 249 j. The 1-2 entry of D7 D. | J am 0) 2: - ok He Came HE Omen “2g ast eo-7r to = 24 Gre jrvoleed ! 4 22 16 94 <—~ geen) 2. Let A= 10 58 51 | andletb= | 228 |. —2.=5 15 —63 2a. Find A~! on your calculator using any method you like. Give your answer in fractions! a. [3754 — -205% 99/6 (4m by cathy Ne ae tl TE La # A, fo = ! a ps 1 2b. Solve Ax = b. Give your answer a . fndiny A] ) se 9B = [SY (ly att (0) » [i 4 15 he ene a) 3. Let A € Mxn. Give four statements which are equivalent to the statement “A is invertible”. (From the invertible matrix theorem). Note that “A~! exists” is not one of them. Hints: span, linearly independent, RREF, solutions of Ax = 0, pivot, solutions of Ax = b, associated linear transformation, ... . The hints an hl a di 3a. The colina of 4 Span IR” r Se, pis ii positions, 2. 1h olinn | A) dom ¢ Ihecl, iebperdire sot] 3h Pa hen at lu The colons 4 eae eer indkep ¢y § je oaeet seer se RAEF (A) = ee, : sd. 7f, only soln JAR =B he trial soln,