Question

1. (20 points) Find the eigenvalues and eigenvectors of [ [A]=left[egin{array}{cc} 10 & 9 \ 2 & 3 end{array} ight] ] using the determinant method 

          1. (20 points)
Find the eigenvalues and eigenvectors of
[
[A]=left[egin{array}{cc}
10 & 9 \
2 & 3
end{array}
ight]
]
using the determinant method
1. (20 points) Find the eigenvalues and eigenvectors of [ [A]=left[eginarraycc 10 9 2 3 endarray ight] ] using the determinant method

Added by Mathias M.

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Linear Algebra and Its Applications
Linear Algebra and Its Applications
David C. Lay, Steven R. Lay, Judi J.… 5th Edition
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Transcript

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00:01 So here we give the matrix 10 9 2 3 and we want to find the eigenvalues and eigenvectors so in order to do that, we want to take the determinant of a minus lambda i which is going to be the determinant of 10 minus lambda times 9 or not times 9 but 9 2 and 3 minus lambda so this determinant is going to be 10 minus lambda times 3 minus lambda minus 2 times 9 which is 18 and we want to set this equal to 0 and from there we can go ahead and multiply these two to get 30 minus 13 lambda plus lambda squared minus 18 equals 0 so we get lambda squared minus 13 lambda plus 12 equals 0 this factors to be lambda minus 12 times lambda minus 1 which implies that lambda equals 12 and lambda equals 1 so those are the two eigenvector eigenvalues to find our eigenvectors we're gonna have to plug in our lambdas into this matrix...
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