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Matrix A=(1 -1
2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I?
2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I?
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Matrix A=(1 -1 2 3) then find the eigen value of matrix b=A^4-3A^3+3A^...
Calculating the Eigenvalues of Matrix B
Given matrix A=(1 -1 2 3), we need to find the eigenvalues of matrix B= A^4 - 3A^3 + 3A^2 - 2A + 8I.
Finding the Matrix A raised to different powers
- A^2 = A*A = (1 -1 2 3)*(1 -1 2 3) = (0 2 5 7)
- A^3 = A^2*A = (0 2 5 7)*(1 -1 2 3) = (12 -10 31 41)
- A^4 = A^3*A = (12 -10 31 41)*(1 -1 2 3) = (21 -21 74 98)
Calculating the Matrix B
Substitute the values of A^4, A^3, A^2, A into the expression B= A^4 - 3A^3 + 3A^2 - 2A + 8I.
Then, B = (21 -21 74 98) - 3*(12 -10 31 41) + 3*(0 2 5 7) - 2*(1 -1 2 3) + 8*(1 0 0 1) = (1 -23 0 12).
Calculating the Eigenvalues of Matrix B
Now, find the eigenvalues of matrix B= (1 -23 0 12).
Det(B - λI) = 0 gives the characteristic equation: λ^2 - 13λ + 24 = 0.
Solving the characteristic equation gives the eigenvalues: λ1 = 3, λ2 = 8.
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Matrix A=(1 -1 2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I?
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Matrix A=(1 -1 2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Matrix A=(1 -1 2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Matrix A=(1 -1 2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I?.
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