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22 November, 16:00

If A=1--21-20find the eigenvalues of the matrix A. Your answer should consist of two integers representing the two eigenvalues. Eigenvalue: Skipped Eigenvalue: Skipped

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  1. 22 November, 16:59
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    Eigenvalue: 0

    Eigenvalue: 3

    Step-by-step explanation:

    For any nxn matrix A, the eigenvalues of A are the y values that respect the following conditions

    det (A - yI) = 0, where I is the order n identity matrix.

    So A = [1 2; 1 2], I = [1 0; 0 1] yI = [y 0; 0 y]. In this notation, i have; as a new line.

    A - yI = [1-y 2; 1 2-y]

    det (A - yI) = (1-y) * (2-y) - 2 = 0

    = 2 - y - 2y + y² - 2 = 0

    = y² - 3y = 0

    = y (y-3) = 0

    y = 0 or y - 3 = 0

    y = 3
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