(1 point) Find the characteristic polynomial of the matrix -2-20 1 -1 0 p(x)
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
(1 point) Find the characteristic polynomial of the matrix. Use x as your variable instead of λ. -3 2
Let p(x) be the polynomial The companion matrix of p(x) is the n x n matrix 1 1 n-2 .. -a-a0 cp) = 10 1 0 Find the companion matrix of p(x) - x3 + 5x2 - 2x 15 and then find the characteristic polynomial of C(p). C(p) det(C(p) Xr)-
Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3 x 3 determinants. [Note: Finding the characteristic polynomial of a 3 x 3 matrix is not easy to do with just row operations, because the variable is involved.] 4 0 | 4 8 1 -2 2 0 -3 The characteristic polynomial is (Type an expression using , as the variable.) Find the characteristic polynomial of the matrix, using either a cofactor expansion...
Problem 2. (a) Let A be a 4 x 4 matrix with characteristic polynomial p(t) = +-12+} Find the trace and determinant of A. 2 e: tr(4) and det(A) = 0 12: tr(A) = 0 and det(A) 2 3 2 T: tr(A) = 0 and det(A) 3 : None of the other answers 01 OW
Q3. Find the characteristic polynomial and the eigenvalues of
the matrix.
Find the characteristic polynomial and the eigenvalues of the matrix. -6 7 -7 3 The characteristic polynomial is (Type an expression usingA as the variable. Type an exact answer, using radicals as needed.)
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2. (a) Find the eigenvalues of A and bases for the corresponding eigenspaces. (b) Determine the geometric and algebraic multiplicities of each eigenvalue and whether A is diagonalizable or not. If it is, give a diagonal matrix D and an invertible matrix S such that A-SDS-1. If it's not, say why not.
Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A - XI is 12 + 72 + 3 A=
Find the characteristic polynomial and the eigenvalues of the matrix. 8 7 -7 - 6 Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3 x 3 determinants. [Note: Finding the characteristic polynomial of a 3 x 3 matrix is not easy to do with just row operations, because the variable A is involved.] 500 -7 3 8 - 5 0 4
Problem #30: [2 marks] Suppose that a matrix A has characteristic polynomial p() = 1 - 31' + 814 - 23. Consider the following statements. (i) i = 2 is an eigenvalue of A. (ii) A is a 4 x 4 matrix. (iii) That same p() is also the characteristic polynomial of A! Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True...