Answer: determinant=0
Explaination: Please see the attached figure for the detailed solution.

Find the determinant of this equation. Problem 11 (10 points). Suppose that the characteristic polynomial of...
11 7 31 (10 points) Find the characteristic equation and all eigenvalues for the matrix A = 0 3 16 4 -2] without using a calculator. Show all of your work. (Hint: Expand the determinant along the row with the most zeros.)
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
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
please do both 1 & 2
() There is interesting relationship2 between a matrix and its characteristic equation that we explore in this exercise. 2 (a) We first illustrate with an example. Let B - 1 -2 i. Show that 2-4 is the characteristic polynomial for B ii. Calculate B2. Then compute B2+ B 412. What do you get? (b) The first part of this exercise presents an example of a matrix that satisfies its own characteristic equation. Explain for...
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.)
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...
Suppose that a matrix A has the characteristic polynomial (1+1)3 (a 1 + 12 + b) for some a, b € R. If the trace of A is 7 and the determinant of A is -24, find all eigenvalues of A. (a) Enter the eigenvalues as a list in increasing order, including any repetitions. For example, if they are 1,1,0 you would enter 0,1,1: (b) Hence determine a: Number (c) and b: Number
Find the characteristic polynomial of A=
Linear Algebra Problem
Complete each of the following. (a) Suppose that A has characteristic polynomial p(\) = 13(2+1)5(1-3)4. In a table, list the eigenvalues of A, along with their algebraic multiplicities. Using this, find the order of A. (b) If A has a ten-dimensional column space, what is the nullity of A? Is A diagonal- izable? Explain.
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