[5-A -1 5 3-λ Find all λ so det -0 (hint: use the quadratic formula).
(a) Use the fact that det(B) =det(BT) for all matrices B to prove that if λ is an eigenvalue of A, then λ is also an eigenvalue of AT. (You may also use the fact that I-I.) (b) Prove that if the sum of the entries in each row of A = 1, then l is an eigenvalue of A. (Hint: What is A?) (c) Use parts a and b to prove that if the sum of the entries in...
Use the quadratic formula to find all degree solutions and θ if 0° ≤ θ < 360°. Use a calculator to approximate all answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 2 sin2 θ − 2 sin θ − 1 = 0
Chapter 5, Section 5.1, Question 24a Find det (A) given that A has p(A) as its characteristic polynomial. det (A) = Hint: See the proof of Theorem 7.1.4. ( If given det (ÀI-A) = λη + C1A + … + cn then, on setting λ 0, det (-A) = cn or (-1)ndet (A) = cn ) Click if you would like to Show Work for this question: Open Show Work n -1
Chapter 5, Section 5.1, Question 24a Find det...
7. 1/4 points | Previous Answers PooleLinAlg4 4.1024. Find all of the eigenvalues λ of the matrix A. (Hint: Use the method of Example 4.5 of finding the solutions to the equation 0 = det(A-ÀI. Enter your answers as a comma-separated list.) -13B 5 0 Give bases for each of the corresponding eigenspaces span (smaller λ-value) (larger λ-value)
Question 23 Find all solutions using estimated degrees to the nearest tenth. Hint: Quadratic Formula sin2x - 3sin x - 1 = 0 B I y A- A - IX E E5 1 x'x, E V VTT TT 12pt Paragraph
for a matrix solution of the quadratic (3) Find a formula of the form x = -B C equation ax2 + bx +c = 0. Here c denotes and 0 denotes 0 0 (Hint: First show how the square root of any number D can be obtained using a where it looks different depending matrix of the form on whether D is negative. Then use the quadratic formula.) positive or
for a matrix solution of the quadratic (3) Find a...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b
3. Find all critical points of dt dt with...
use the definition of the characteristic polynomial for now on.
χA(λ) = det(λI − A).
1. Find an invertible matrix P and a diagonal matrix D such that A = PDP-1 where
Use the quadratic formula to solve the equation x² - 2x+1=0
6x2-x-1 = 0 7. Use quadratic formula to solve.