F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eige...
3. Eigenvalues. Consider the symmetric matrix 3 1 0 A=112 0 1 4/5 (a) How many eigenvalues of A are between 3 and 0? (Don't explicitly compute them. It will take too long.) (b) Is A positive definite? Why? 3. Eigenvalues. Consider the symmetric matrix 3 1 0 A=112 0 1 4/5 (a) How many eigenvalues of A are between 3 and 0? (Don't explicitly compute them. It will take too long.) (b) Is A positive definite? Why?
= ) 1 5 # 4 [10 points] Recall the real symmetric 2 by 2 matrix B of # 3. 5 1 # 4 a) From the matrix fact sheet, what are the eigenvalues of B and its characteristic polynomial ? # 4 b) Compute the trace of B, the sum of diagonal terms of the matrix B in three ways. 1- directly, 2- via eigenvalues, 3-via characteristic polynomial # 4 c) Compute the determinant of B, ad — bc,...