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

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Chapter2: Second-order Linear Odes
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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
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).
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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