9.18 Invertible (none of the eigenvalues are zero). det(A) = −12, Tr(A) = 1. 2 det(A-¹) = -2, Tr(A-¹) = 1 + - = - 12
9.18 Invertible (none of the eigenvalues are zero). det(A) = −12, Tr(A) = 1. 2 det(A-¹) = -2, Tr(A-¹) = 1 + - = - 12
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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I'm facing difficulties in solving this problem using only matrix notation, and I'm looking for your help. The requirement is to find a solution using matrix notation exclusively, without employing any alternative methods. Could you please provide me with a detailed, step-by-step explanation in matrix notation, guiding me towards the final solution?
![9.18 Invertible (none of the eigenvalues are zero). det(A) = -12, Tr(A) = 1.
det(A-¹) = -2, Tr(A-¹) = 1
+
+1-1-
NİM](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0113a2ae-503a-4a14-a5d4-d8fff765856f%2F26e57975-79a0-4ac4-b76a-b6f577b9b64f%2Fjk854k_processed.png&w=3840&q=75)
Transcribed Image Text:9.18 Invertible (none of the eigenvalues are zero). det(A) = -12, Tr(A) = 1.
det(A-¹) = -2, Tr(A-¹) = 1
+
+1-1-
NİM
![9.18. Let A be a 3 x 3 matrix whose eigenvalues are 1₁ = 2,12 = 2,A3 = -3. Is
the matrix A invertible? Find det(A) and Tr(A). If A is invertible, find det(A-¹)
and Tr(A-¹).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0113a2ae-503a-4a14-a5d4-d8fff765856f%2F26e57975-79a0-4ac4-b76a-b6f577b9b64f%2F7lsba3n_processed.png&w=3840&q=75)
Transcribed Image Text:9.18. Let A be a 3 x 3 matrix whose eigenvalues are 1₁ = 2,12 = 2,A3 = -3. Is
the matrix A invertible? Find det(A) and Tr(A). If A is invertible, find det(A-¹)
and Tr(A-¹).
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