- #1
says
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Homework Statement
Determine if the matrix is diagonalizable or not.
A=
[ 3 -1 ]
[ 1 1 ]
Homework Equations
Eigenvalues = det(A-Iλ)
determinant of a 2x2 matrix = ad-bc
The Attempt at a Solution
Eigenvalues = det(A-Iλ)
[ 3 -1 ] - [ λ 0 ] = [ 3 -λ -1 ]
[ 1 1 ] [ 0 λ ] [ 1 1-λ ]
det =
(3 -λ*1-λ) -1*(-1)
λ2-4λ+4
(λ-2)(λ-2) = 0
λ = 2
Only one eigenvalue -- for this matrix A to be diagonalizable we need two eigenvalues so that
D=
[ λ1 0 ]
[ 0 λ2 ]
where λ1 and λ2 are 2 eigenvalues.
Am I correct in my assumptions?