1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix...
The symmetric matrix A below has distinct eigenvalues 10,-2 and-8. Find an orthogonal matrix P and a diagonal matrix D such that pTAP-Duse the square root symbol 'where needed to give an exact value for your answer. -1 47 A- 4 2-4 0 0 0] P=10 0 0| D=10 0 0
7. Orthogonally diagonalize the matrices by finding an orthogonal matrix Q and a diagonal matrix D such that QT AQ = D. 1 А 0 -1 0 0 -1 0 1 В = 2 0 0 1 0 1 0 0 0 0 1 0 1 0 0 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...
Will rate and comment. Thank you ! Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper diagonal form. (Enter each matrix in the form [row 1, [row 2], ...], where each row is a comma-separated list.) 42 €34) A-O 0 2 4 o o 42 (P, PTAP) Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper diagonal form. (Enter each matrix in the form [row 1,...
(f) Let A be symmetric square matrix of order n. Show that there exists an orthogonal matrix P such that PT AP is a diagonal matrix Hint : UseLO and Problem EK〗 (g) Let A be a square matrix and Rn × Rn → Rn is defined by: UCTION E AND MES FOR THE la(x, y) = хтАУ (i) Show that I is symmetric, ie, 14(x,y) = 1a(y, x), if a d Only if. A is symmetric (ii) Show that...
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. Enter the matrices P and D below. 1 1 (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D 9 3 3 9 Enter the matrices P and D below.
7.1.21 Question Help Orthogonally diagonalize the matrix, giving an orthogonal matrix and a diagonal matrix D. To save time, the eigenvalues are 17, 13, and 1. 8 7 1 1 Enter the matrices P and D below. 0 0 22 2 3 0 0 1 0 0 0 0 1 0 0 0 0 13 0 0 0 0 17 - 1 1 1 (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do...
[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...
please answer the five questions clearly. I have provided the data. 7 Diagonal Matrices Diagonal Matrices If A = (a) is a square matrix, then the entries and are called diagonal entries. A square matrix is called diagonal if all non-diagonal entries are zeros. Explore what happens if we add, subtract or multiply diagonal matrices. A and B are the same matrices in previous sections ( section 5.) Type D-diag(diag(A)) to create a diagonal matrix from A. Type E-diag(diag(B)) to...