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Exercise 7.1. If Bk is a symmetric nonsingular matrix, compute the update for M = B , where 1 Bdk)(kBd7. Вк+1 3 Вк + (y...
Exercise 10. Write A = 1-3 6 01 as the sum of a symmetric matrix B and a skew-symmetric matrix C. SVImImetric matrIX C
3 -2 3 Find a nonsingular matrix P such that P-1AP is diagonal where A = 0 3 -2 0-3 2
For a matrix A 3 5 (a) Find a nonsingular matrix Q let D-AQ be a diagonal matrix b)Find the inverse of A 氿ㄧ '11.ril. IfA+小1, find the maximal and minin al values of毗孵. 2 For a matrix A 3 5 (a) Find a nonsingular matrix Q let D-AQ be a diagonal matrix b)Find the inverse of A 氿ㄧ '11.ril. IfA+小1, find the maximal and minin al values of毗孵. 2
4 Consider the following nonsingular matrix P = a) Find P by hand. by hand. b) Use P and P-1 to find a matrix B that is similar to A c) Notice that A is a diagonal matrix (a matrix whose entries everywhere besides the main diagonal are 0). As you may recall from #5 on Lab 2, one of the many nice properties of diagonal matrices (of order n) is that 0 1k 0 a11 0 0 a11 0...
1. Writ A as the sum of Ma symmetric matrix and Na skew-symmetric matrix. 1 24 A=430= M+N 865 where, MT M and N-N. A+A Conclusion: M = and N= 2
[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP-D,where D is a diagonal matrix with the characteristic roots of A on the diagonal. Show that PA P is also a diagonal matrix. (b) Let A be an m × n matrix of rank m such that A = BC where B and C each has rank m. Show that (BC) CB. 16 STA4801/101/0/2019 (c) For the matrix...
Q1. Determine if the matrix B is singular or nonsingular and explain why. 1 2 11 B = 0 3 6 to 3 3
5. Recall that a symmetric matrix A is positive definite (SPD for short) if and only if T Ar > O for every nonzero vector 2. 5a. Find a 2-by-2 matrix A that (1) is symmetric, (2) is not singular, and (3) has all its elements greater than zero, but (1) is not SPD. Show a nonzero vector such that zAx < 0. 5b. Let B be a nonsingular matrix, of any size, not necessarily symmetric. Prove that the matrix...
[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP-D,where D is a diagonal matrix with the characteristic roots of A on the diagonal. Show that PA P is also a diagonal matrix. (b) Let A be an m × n matrix of rank m such that A = BC where B and C each has rank m. Show that (BC) CB. 16 STA4801/101/0/2019 (c) For the matrix...
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?