Quiz VII1. The matrixA=⎛⎝201010102⎞⎠is symmetric. Find a basis forR3consisting ofeigenvectors forA.Solution:SinceAis symmetric,there will beanorthonormalbasis consisting ofeigenvectors ofA, but you do not need to use that to solve the problem. First findthe eigenvaluesdet⎛⎝2−λ0101−λ0102−λ⎞⎠= (2−λ)2(1−λ)−(1−λ) = (1−λ)(3−4λ+λ2).So the eigenvalues are 3 and 1.Solving for the eigenspaces,v1=⎛⎝101⎞⎠is aneigenvector for the eigenvalue 3. For the eigenvalue 1,A−I=⎛⎝101000101⎞⎠,and the reduced row echelon form of that is just
This is the end of the preview.
access the rest of the document.