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

This is the Quiz Solution of Linear Algebra. Mainly includes points are Explicit Conditionsm, Expansion Across, Equilibrium Prices, Equation, Elementary, Elementary Row etc. Key important points of tags are: Column Space, Row Equivalent, Matrix, Dimension, Null Space, Basis, Row Space, Maximum, Minimum, Dimensions

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

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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.