Column Space - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 2054 Quiz 7, page 1 November 16, 2007 = NAME, ee gosta Solns Qed 4--l =-2.=3 10-304 —-5 00 0 De OS a0) Oe a SOS ae 1. Fact: The matrix A= | 4 0 -12 9 34 25 | isrowequivalentto|0 0 012 5 36 15 O 12 .-3 090 000 0 24 10 0 8 -2 00° 08-00" Oo 1A. Find each of the following: i) The rank of A. = aim eal Space 3) ii) The dimension of the null space of A. who, @ iii) A basis for the column space of A. iv) A basis for the row space of A. The pri. caunns 4 A form basit, Ao dscosse® The. pron -2eve pot Hw KREF fen if evr tyr. 4 h amg 2 fhelfelle fave 6 bawr lor booth it. (the he) tifela Al » ie Ty tee es o ally 2. rhe Wns, be ware! The cocryporih . [A Mieran hor i {ie ° “ke 4 th 2. Suppose BE Mays. ae dor golf) | boo oz sf 3 2A. What are the maximum and minimum possible dimensions for Pleat ? MAX: MIN: (2) din (wol(@)) = # 1 tree vanwbles TF Bx te zero matrri, al vides ac Be 3 3 ros, 4 2 var i. 2B. What are the maximum and minimum be shee tye arg 0 Pe rank at B? MAX: ewe TiN: oO rank = # gf phot cabmns. The a 30 Uf Baal 2) @ 7 iecee| ES lok He mawnom a te bjs 3 ' ae vy (rank(B)) = S— sai csttmimatctc, (mk A le)

) #20 =) 4d 32420 ( ) ° | = ATR AIL 3B. Find the eigenvalues of C' using the answer to (3A). ng d= YATILAO setting (a-6)r +2) =O fo He exyenvales Ae +6 and ~Z. 3C. Find an eigenvector of © corresponfing to the larger of the twa eigenvalues in (3B). 6 te larger. We need sot f CR OR of [ane -10 4 lel 7 | -5 8G s 2\e -|o -% 2 i, : * “Vs s[o] - [5 5 | oe Ka%hxe Whee he is eo ah c vy eigen veces Phone fre have te hrm | | fu pe Extn SED.