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

This is the Quiz Solution of Linear Algebra. Mainly include Row Operation, Resulting Matrix, Requirements, Reduced Row Echelon, Reason, Particular Solution etc. Key important points of tags are: Number of Entries, Values, Give the Reason, Product, Entry, Matrix Product, Size, Method, Answer, Statements

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

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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,