Determinants - Linear Algebra - Solved Exam, Exams of Linear Algebra

This is the Solved Exam of Linear Algebra which includes Empty, Unique Solution, Contains, Equation, Solution, Calculations, Possible, Solution, Set, Three Vectors etc. Key important points are: Determinants, Properties, Obtained, Interchanging, Invertible, Factorization, Equation, Formula, Invertible, Using Pivots

Typology: Exams

2012/2013

Uploaded on 02/27/2013

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No Math 205 Section B : Test 2 (50 points) Name: Sol whons * Check that you have 6 questions on three pages. « Show all your work to receive full credit for a problem. 1. (10 points) Let A and B be 4x 4 matrices, with det A = —10 and det B = 6. Use properties of determinants to compute: (a). det-A?BT dot (BT) = cet (A) det (A). det (BT) —dek CA) det (A) deb CB) = tI (10: CO) = jeoo] (6) det2B Bas G rews; for each wo kine cooled hoy ao faker of 2 Cy det 2B = 2 debt =f96} deferrnmant qe (c) det. C where C is obtained from A by interchanging rows 2 and 4 et C=~det A =[lo] (d) det (B?)-# if B? is invertible. Otherwise, explain why B? is not invertible. det BE #O- So B ts inverbble. ( Br sy inverble, as ik ore the produc of taro. Invevbble. malizes oe _[L). dae) = ie are) (et 8) Stl