Let A = [ 0 2 0 1 0 2 0 1 0 ]  . (a)...

Let A = [ 0 2 0

1 0 2

0 1 0 ]  .

(a) Find the eigenvalues of A and bases of the corresponding eigenspaces.

(b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line.

(c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist.

(d) Write down explicitly a diagonalizing matrix S, and a diagonal matrix Λ such that S −1AS = Λ; A = SΛS −1 . or explain why A is not diagonalizable.

Expert Solution

(a)

Colby Messinger answered 1 year ago

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly a diagonalizing...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly a diagonalizing...

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a...

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a system of two equations in four unknowns whose solution set is spanned by X and Y. (b) Find a system of three equations in four unknowns whose solution set is spanned by X and Y. (c) Find a system of four equations in four unknowns that has the set of vectors of the form Z + aX + bY as its general solution where...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2, f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the Lagrange interpolation F(x, y) that interpolates the above data. Use Lagrangian bi-variate interpolation to solve this and also show the working steps.

Let G = Z4 ⊕ Z4, and H = {(0, 0), (2, 0), (0, 2), (2,...

Let G = Z4 ⊕ Z4, and H = {(0, 0), (2, 0), (0, 2), (2, 2)}, and K = (1, 2). Is G/H isomorphic to Z4 or Z2 ⊕ Z2? Is G/K isomorphic to Z4 or Z2 ⊕ Z2?

Let ?1 and ?2 have the joint pdf f (?1, ?2)= 6?2 0<?2<?1<1 =0 else where...

Let ?1 and ?2 have the joint pdf f (?1, ?2)= 6?2 0<?2<?1<1 =0 else where A. Find conditional mean and conditional variance ?1given?2 . B. Theorem of total mean and total variance?1given?2 .(urgently needed)

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1,...

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1, 2] with R 2 1 f(x)dx = 2 3 . Prove that f(x 2 ) is integrable on [1, √ 2] and √ 2 6 ≤ Z √ 2 1 f(x 2 )dx ≤ 1 3 .

Let C be the following matrix: C=( 1 2 3 -2 0 1 1 -2 -1...

Let C be the following matrix: C=( 1 2 3 -2 0 1 1 -2 -1 3 2 -8 -1 -2 -3 2 ) Give a basis for the row space of Cin the format [1,2,3],[3,4,5], for example.

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

2. Let {Zt , t = 0, ±1, ±2, ...} be a sequence of independent random...

2. Let {Zt , t = 0, ±1, ±2, ...} be a sequence of independent random variables, each with mean EZt = 0 and variance Var(Zt) = σ 2 . Define Xt = ZtZt−1 + Zt−2. • Compute the mean and the covariance function for Xt . • Is {Xt} weakly stationary? Explain why.

Question

Let A = [ 0 2 0 1 0 2 0 1 0 ]  . (a)...

Solutions

Expert Solution

Related Solutions

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let G = Z4 ⊕ Z4, and H = {(0, 0), (2, 0), (0, 2), (2,...

Let ?1 and ?2 have the joint pdf f (?1, ?2)= 6?2 0<?2<?1<1 =0 else where...

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1,...

Let C be the following matrix: C=( 1 2 3 -2 0 1 1 -2 -1...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

2. Let {Zt , t = 0, ±1, ±2, ...} be a sequence of independent random...