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4 2 3 13. Find a basis for the eigenspace of the matrix A1 1- corresponding to the 2 49 eigenvalue -3. [4 points.]

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Your input: find the eigenvalues and eigenvectors of 4 23 1 1 -3 2 49 Start from forming a new matrix by subtracting A from tSolve the equation 81 + 36 0 Roots are: These are eigenvalues Next, find eigenvectors.3 4 Perform row operations to obtain rref of the matrix:「1 2 3 1 -2 -3 (for 24 6 「1 2 3 し0 0 0Add row 1 to row2 (R2 -R2 +R1): Γι 2 31 2 4 6 Subtract row 1 multiplied by 2 from row 3 (R3 R3 (2) Ri):0 then v -3s - 2t. Therefore, V- 0

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