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# Problem Consider the matrix A =HShow that 1s a eigenvalue of A with algebraic multiplicityDetermine the geometric multiplicity of this eigenvalueFind basis for the ...

## Question

###### Problem Consider the matrix A =HShow that 1s a eigenvalue of A with algebraic multiplicityDetermine the geometric multiplicity of this eigenvalueFind basis for the eigenspace E3 (A-30).Find bases for 3I)2 and (A 31)3 s0 that your basis for 3I)k includes your basis for 31)*-1_ Do this by solving 3Jv = and (A 3[Jw where is an eigenvector in E3. Note that if your second basis already has vectors there won't be any additional vectors in the third basislForm the matrix whose columns are the thre

Problem Consider the matrix A = H Show that 1s a eigenvalue of A with algebraic multiplicity Determine the geometric multiplicity of this eigenvalue Find basis for the eigenspace E3 (A-30). Find bases for 3I)2 and (A 31)3 s0 that your basis for 3I)k includes your basis for 31)*-1_ Do this by solving 3Jv = and (A 3[Jw where is an eigenvector in E3. Note that if your second basis already has vectors there won't be any additional vectors in the third basisl Form the matrix whose columns are the three vectors in Four basis for E3 and compute Notice that you order the columns of in the most logical way; will be triangularl 5-'AS. Solve the system y = Jy: Find the solution to 1 Ar by multiplying by the appropriate matrix  #### Similar Solved Questions

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