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IfA=[] is an nxn matrix, then the trace Tr A of A is defined to be Tr A-a₁a22. The characteristic polynomial p(A)- A- of a 3x3 matrix A is given by (det A). The remaining coefficient e, can be found by substituting A-1 and then calculating the two determinants (A) and p(1)-(A-1). Use this P(A)-(Tr A²+₁ method to find the characteristic polynomial, eigenvalues, and associated eigenvectors of the following matrix. 75 20-112 A 17 12 -28 48 18-72 The characteristic polynomial is p(A) - (Type an expression using à as the variable.)

IfA=[] is an nxn matrix, then the trace Tr A of A is defined to be Tr A-a₁a22. The characteristic polynomial p(A)- A- of a 3x3 matrix A is given by (det A). The remaining coefficient e, can be found by substituting A-1 and then calculating the two determinants (A) and p(1)-(A-1). Use this P(A)-(Tr A²+₁ method to find the characteristic polynomial, eigenvalues, and associated eigenvectors of the following matrix. 75 20-112 A 17 12 -28 48 18-72 The characteristic polynomial is p(A) - (Type an expression using à as the variable.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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IfA=[] is an nxn matrix, then the trace Tr A of A is defined to be Tr A-a₁₁ + a22+ The characteristic polynomial p(3)= |A- of a 3x3 matrix A is given by P(2)-3(TrA)²+₁+ (det A). The remaining coefficient c, can be found by substituting A-1 and then calculating the two determinants (A and p(1)- (A-1). Use this method to find the characteristic polynomial, eigenvalues, and associated eigenvectors of the following matrix 75:20-112 A 17 12 -28 48 18-72 The characteristic polynomial is p(x) = (Type an expression using à as the variable.)
Transcribed Image Text:IfA=[] is an nxn matrix, then the trace Tr A of A is defined to be Tr A-a₁₁ + a22+ The characteristic polynomial p(3)= |A- of a 3x3 matrix A is given by P(2)-3(TrA)²+₁+ (det A). The remaining coefficient c, can be found by substituting A-1 and then calculating the two determinants (A and p(1)- (A-1). Use this method to find the characteristic polynomial, eigenvalues, and associated eigenvectors of the following matrix 75:20-112 A 17 12 -28 48 18-72 The characteristic polynomial is p(x) = (Type an expression using à as the variable.)
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