Suppose we have a matrix A: 2 1 0 A = 1 4 0 0 3...

 

Transcribed Image Text:

Suppose we have a matrix A: 2 1 0 A = 1 4 0 0 3 10 (1) 1. Find the L1 and L∞ norms of A (Points: 15) 2. Show the details of evaluating eigenvalues of A, the L2 norms of A and A-¹. Numbers you may need: √2≈ 1.414 and √8≈ 2.828. Note: use pre-programmed functions such as 'eig' in MATLAB, 'eigen- values()' in C++, and 'eigvals' in Python would get few credits. (Point: 25) 3. Evaluate the condition number of matrix A based on the resulting L2 norms of A and A-1 (Point: 10) Note: use pre-programmed functions, such as 'cond' in MATLAB and the like, would get few credits. Activate W Go to Settings Suppose we have a matrix A: 2 1 0 A = 1 4 0 0 3 10 (1) 1. Find the L1 and L∞ norms of A (Points: 15) 2. Show the details of evaluating eigenvalues of A, the L2 norms of A and A-¹. Numbers you may need: √2≈ 1.414 and √8≈ 2.828. Note: use pre-programmed functions such as 'eig' in MATLAB, 'eigen- values()' in C++, and 'eigvals' in Python would get few credits. (Point: 25) 3. Evaluate the condition number of matrix A based on the resulting L2 norms of A and A-1 (Point: 10) Note: use pre-programmed functions, such as 'cond' in MATLAB and the like, would get few credits. Activate W Go to Settings Suppose we have a matrix A: 2 1 0 A = 1 4 0 0 3 10 (1) 1. Find the L1 and L∞ norms of A (Points: 15) 2. Show the details of evaluating eigenvalues of A, the L2 norms of A and A-¹. Numbers you may need: √2≈ 1.414 and √8≈ 2.828. Note: use pre-programmed functions such as 'eig' in MATLAB, 'eigen- values()' in C++, and 'eigvals' in Python would get few credits. (Point: 25) 3. Evaluate the condition number of matrix A based on the resulting L2 norms of A and A-1 (Point: 10) Note: use pre-programmed functions, such as 'cond' in MATLAB and the like, would get few credits. Activate W Go to Settings