In: Advanced Math

Let A =

2 | 0 | 1 |

0 | 2 | 0 |

1 | 0 | 2 |

and eigenvalue λ1 = 3 and associated eigenvector v(1) = (1, 0, 1)t . Find the second dominant eigenvalue λ2 (or the approximation to λ2) by the Wielandt Dflation method

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...

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 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 ? be an eigenvalue of a matrix A. Explain why dim(?) ? 1

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...

Find the basic eigenvectors of A corresponding to the eigenvalue
λ.
A =
−1
−3
0
−3
−12
35
4
36
−3
9
0
9
12
−37
−4
−38
, λ =
−1
Number of Vectors: 1
⎧
⎨
⎩⎫
⎬
⎭
0
0
0

Which of the following statements is/are true?
1) If a matrix has 0 as an eigenvalue, then it is not
invertible.
2) A matrix with its entries as real numbers cannot have a
non-real eigenvalue.
3) Any nonzero vector will serve as an eigenvector for the
identity matrix.

Let v1 be an eigenvector of an n×n matrix A corresponding to λ1,
and let v2, v3 be two linearly independent eigenvectors of A
corresponding to λ2, where λ1 is not equal to λ2. Show that v1, v2,
v3 are linearly independent.

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

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- A. How do media play a role in perpetuating racial stereotypes? B. How does popular culture...
- Consider the following marginal benefit (demand) curves of two individuals for a certain good: MBA(q) =...
- In Python syntax, create a list of 10 numbers (any numbers). Create your list 3 times,...
- 1. A galvanic cell is based on the following half-reactions at 285 K: Ag+ + e-...
- the following techniques for analyzing projects: Payback Rule Discounted Payback Period Net Present Value Internal Rate...
- 1. Describe the primary issues of adolescence according to Erikson. Be sure to comment on issues...
- 6. A person holds a rifle horizontally and fires at a target. The bullet has a...

ADVERTISEMENT