Please help! Will rate! 1. [7pts) Let [ 3 1 -2] 1AlleAmax (ATA) A= ? P(ATA)-...
linear algebra 1 1 2. Let A= 1 -1 2 0 -1 1 (a) Find the characteristic polynomial of A. You do not need to factor. (b) Verify that 71 0 4 is an eigenvector of A and identify the associated eigenvalue 11. 2 (C) Given that 12 = 2 is an eigenvalue of A, find a basis for its corresponding eigenbasis.
Problem 5: Let A be the following matrix: 2 -3 1] A= 1 -2 11 1 -3 2 (a) Compute the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) For each eigenvalue of A, find a corresponding eigenvector.
Let A be an n × n matrix with characteristic polynomial f(t)=(−1)nt n + an−1t n−1 + ··· + a1t + a0. (a) Prove that A is invertible if and only if a0 = 0. (b) Prove that if A is invertible, then A−1 = (−1/a0)[(−1)nAn−1 + an−1An−2 + ··· + a1In]. 324 Chap. 5 Diagonalization (c) Use (b) to compute A−1 for A = ⎛ ⎝ 12 1 02 3 0 0 −1 ⎞ ⎠ . #18 a, b...
Q5 8 Points Let A = -4 0 -3 2 3 0 -2 -1 3 Q5.1 6 Points Compute PTA (x) (the characteristic polynomial of TA), Write monomials in descending order of their exponent, x^n for 3" and a/b for Example: 5/2 (polynomial of degree 0) -2x+1/3 (polynomial of degree 1) 2x^2-3x+12 (polynomial of degree 2) Enter your answer here give the eigenvalue(s) of TA (in ascending order if multiple exists, separated by a comma and with a blank after...
Only need help on Question 1 a) to h) 2) Let V- [ae" + bxe" | a, b are real numbers]. 3) Let V-[a sin x + b cosz + ce" | a, b, c are real numbers] 1) LetV [ae" + be2"a, b are real numbers ] Let(Df)(x) For each of the three vector spaces V listed in 12, 3 below show that: a) D:V → V and D is a linear transformation b) By differentiation prove the functions...
3. Let L be the linear transformation on R2 that reflects each point P across the line y kx (k>0) a) (2 marks) Show that v and v2 - 1 are eigenvectors of L. b) (1 mark) What is the eigenvalue corresponding to each eigenvector? (Hint: No need to calculate the characteristic polynomial or solve a matrix equation. Geometric reasoning should suffice to solve this problem. Drawing a diagram is recommended!) 3. Let L be the linear transformation on R2...
please help a) Let (1 2 2 A= 2 -2 1 1-8 -4 -7) Calculate AP, and hence find a quadratic polynomial m(2) such that m(A) = 0.
0 4 -1 1 5. Given, A--2 6 -11 L-2 8-3 1 has the characteristic polynomial p(λ)-(x + 2) (z-2)2(z-1) Find the corresponding eigenvector for each eigenvalue 0 4 -1 1 5. Given, A--2 6 -11 L-2 8-3 1 has the characteristic polynomial p(λ)-(x + 2) (z-2)2(z-1) Find the corresponding eigenvector for each eigenvalue
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
3. Let L be the linear transformation on R2 that reflects each point P across the line y kx (k> 0) are eigenvectors of L a) (2 marks) Show that v1 and vz b) (1 mark) What is the eigenvalue corresponding to each eigenvector? (Hint: No need to calculate the characteristic polynomial or solve a matrix equation. Geometric reasoning should suffice to solve this problem. Drawing a diagram is recommended!) 3. Let L be the linear transformation on R2 that...