The symmetric matrix A below has distinct eigenvalues 10,-2 and-8. Find an orthogonal matrix P and...
The symmetric matrix A below has eigenvalues 15 and -15 (multiplicity 2). Find an orthonormal basis B of Rd consisting of eigenvectors of A. Use the square root symbol 'V' where needed to give an exact value for your answer. 5 -5 -10 10 A = -10 -5 -10 | 10 -10 -5] B= 0, 0,
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а) А — 1 0 1 -1 1 0 2 -2 (Ъ) А %— -2 -2 -4 -2 2 |3 0 7 0 5 0 7 0 3 (с) А %— 1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а)...
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0-1 0-1 0 -107 Find the characteristic polynomial of A. far - 41 - Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12, 13) = Find the general form for every eigenvector corresponding to 11. (Uses as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x2 = (0.t,0)...
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0 -1 0-1 0 - 1 0 5 Find the characteristic polynomial of A. - A - Find the eigenvalues of A. (Enter your answers from smallest to largest.) (1, 12, 13) = ]) Find the general form for every eigenvector corresponding to N. (Uses as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your...
[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...
linear algebra Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal -1 0-1 0-1 0 - 1 0 9 1 Find the characteristic polynomial of A. |x - Al- Find the eigenvalues of A. (Enter your answers from smallest to largest.) (21, 22, 23) Find the general form for every eigenvector corresponding to 21. (Uses as your parameter.) X1 - Find the general form for every elge vector corresponding to Az. (Uset as your...
(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...
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is the determinant of A. (b) If a 2 x 2 matrix satisfies tr(AP) = 5, tr(A) = 3, then find det(A). (The trace of a square matrix A, denoted by tr(A), is the sum of the elements on the main diagonal of A.
Find the matrix A of the quadratic form associated with the equation. 48x2 + 72xy + 27y2 - 74x - 52y + 70 = 0 A = Find the eigenvalues of A. (Enter your answers as a comma-separated list.) a = Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) P=
Find the matrix A of the quadratic form associated with the equation. 6x2 - 9xy - 6y2 + 5 = 0 A= Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 2 = Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...), where each row is a comma-separated list.) P = Need Help? Read It Talk to a Tutor