Question
In: Advanced Math
A = ⌈ 1 2 0 ⌉ | -1 0 1 | ⌊ 0 1 -1...
| A = |
|
and | B = |
|
|---|
- Given matrices A and B, find AB and BA. Show all work. Are they equal, and why or why not?
Solutions
Colby Messinger answered 1 year agoRelated Solutions
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2.
3. 4.
A.)MEAN –
B.)MEDIAN -
C.)MODE -
D.)STANDARD DEVIATION –
E.)5 NUMBER SUMMARY –
F.)BOX AND WHISKERS PLOT –
G.) OUTLIERS-
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2.
3. 4.
A.)5 NUMBER SUMMARY –
B.)BOX AND WHISKERS PLOT –
C.) OUTLIERS-
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...
Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2,...
Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2, 2; 0,
0, 0, 1]. Find P, so that P^(-1) A P is in Jordan normal form.
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...
A= 1 0 -7 7 0 1 0 0 2 -2 10 -7 2 -2 2...
A=
1
0
-7
7
0
1
0
0
2
-2
10
-7
2
-2
2
1
Diagonalize the matrix above. That is, find matrix D and a
nonsingular matrix P such that A = PDP-1 . Use the
representation to find the entries of An as a function
of n.
Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1...
Given a matrix A = [?1 ? ?
0 ?2 ?
0 0 ?2], with ?1 ≠ ?2 and ?1, ?2 ≠ 0,
A) Find necessary and sufficient conditions on a, b, and c
such that A is diagonalizable.
B) Find a matrix, C, such that C-1 A C = D, where D is
diagonal.
C) Demonstrate this with ?1 = 2, ?2 = 5, and a, b, and c
chosen by you, satisfying your criteria from A).
2. Given A = | 2 1 0 1 2 0 1 1 1 |. (a)...
2. Given A = | 2 1 0 1 2 0 1 1 1 |.
(a) Compute eigenvalues of A.
(b) Find a basis for the eigenspace of A corresponding to each
of the eigenvalues found in part (a).
(c) Compute algebraic multiplicity and geometric multiplicity of
each eigenvalue found in part (a).
(d) Is the matrix A diagonalizable? Justify your answer
A= 1 2 4 0 1 -2 -1 0 1 2 0 3 8 1 4...
A=
1
2
4
0
1
-2
-1
0
1
2
0
3
8
1
4
. Let W denote the row space for A.
(a) Find an orthonormal basis for W and for W⊥.
(b) Compute projW⊥(1 1 1 1 1 ).
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