UW Common Math 308 Section 5.1 - CHING FUNG CHUI Math 308,...

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Current Score :41 / 41Due :Wednesday, December 2 2015 09:30 AM PST1.2/2 points |Previous AnswersHoltLinAlg1 5.1.004.Findfor the given matrixA.M23=0-50050211[0, -5, 0; 0, 5, 0; 2, 1, 1]M31=-5304-40141[-5, 3, 0; 4, -4, 0; 1, 4, 1]Solution or ExplanationUW Common Math 308 Section 5.1 (Homework)CHING FUNG CHUIMath 308, section A, Fall 2015Instructor: Hon Leung Lee TAWebAssignThe due date for this assignment is past.Your work can be viewed below, but no changes can be made.Important!Before you view the answer key, decide whether or not you plan to request an extension. Your Instructormaynotgrant you an extension if you have viewed the answer key. Automatic extensions are not granted if you haveviewed the answer key.Request ExtensionM23andM31A=053064400540214 1M23=M31=05005021 153044014 1
2.2/2 points |Previous AnswersHoltLinAlg1 5.1.008.FindC13andC22for the given matrixA.931910
3.4/4 points |Previous AnswersHoltLinAlg1 5.1.014.Find the determinant for the given matrixAin two ways, by using cofactor expansion along theindicated row or column.(a) along the first rowdet(A) =33(b) along the third columndet(A) =33Use the determinant to decide ifis invertible.SinceAisisinvertible, and henceTisisinvertible.Solution or Explanation(a) Using the first row,(b) Using the third column,SinceAis invertible, and henceTis invertible.A=5160150 14 50 10 150T(x) =A(x)det(A)0,det(A) =a11C11+a12C12+a13C13+a14C14=(5)C11+ (1)C12+ (6)C13+ (0)C14=(5)(1)1 + 1|M11| + (1)(1)1 + 2|M12| + (6)(1)1 + 3|M13|=(5)(1)+ (6)=3.501501150101401050151451010det(A) =a13C13+a23C23+a33C33+a43C43=(6)C13+ (0)C23+ (0)C33+ (5)C43=(6)(1)1 + 3|M13| + (5)(1)4 + 3|M43|=(6)(5)=3.151451010510151451det(A)0,
4.2/2 points |Previous AnswersHoltLinAlg1 5.1.030.Find all real values ofasuch that the given matrix is not invertible. (HINT: Think determinants, notrow operations. Enter your answers as a comma-separated list. If an answer does not exist, enterDNE.)
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Term
Winter
Professor
Milakis
Tags
Math, Linear Algebra, Algebra, Characteristic polynomial, Invertible matrix, Triangular matrix, Det

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