Question
In: Math
Consider the matrix B = −1 1...
Consider the matrix B =
−1 1 1 2
−1 1 0 3
−2 2 1 −4
(a) Find ||B||F.
(b) It can be shown (See Saito, Lecture Notes, 5.7) that the 1-norm of a matrix A ∈ Rm×n can be written as ||A||1 = max 1≤j≤n||aj||1 whereaj is the jth column of A. Find||B||1.
(c) Find ||B||2.
(d) It can be shown (See Saito, Lecture Notes, 5.9) that the ∞-norm of a matrix A ∈ Rm×n can be written as kAk∞ = max
Solutions
milcah answered 2 years agoRelated Solutions
Consider the matrix of Hibert H100 and the system HX = b, where b is a...
Consider the matrix of Hibert H100 and the
system HX = b, where b is a column
vector from 1 to 100. Solve the system in the following three ways
-->
1) X = H-1 b
2) Using the factorization H = LU
3) Using the factorization H = QR
Premultiplica H for each of the three solution vectors
and make the comparison with vector b.
What method gives a better solution?
Determine the Kernel of matrix B. Determine the Cokernel of matrix B.
Matrix A
1
2
1
3
1
-1
1
2
2
4
1
3
3
2
1
-1
Matrix B
1
2
3
-2
-1
2
2
-1
2
3
2
-3
3
1
2
-1
3
-5
5
5
5
-7
7
-4
Determine the Kernel of matrix B.Determine the Cokernel of matrix B.Determine the row space of the Cokernel of B.Determine the inverse of matrix A.
Perform LU (or PLU) factorization on matrix A and determine the L...
Let B equal the matrix below: [{1,0,0},{0,3,2},{2,-2,-1}] (1,0,0 is the first row of the matrix B)...
Let B equal the matrix below:
[{1,0,0},{0,3,2},{2,-2,-1}]
(1,0,0 is the first row of the matrix B)
(0,3,2 is the 2nd row of the matrix B
(2,-2,-1 is the third row of the matrix B.)
1) Determine the eigenvalues and associated eigenvectors of B.
State both the algebraic and geometric multiplicity of the
eigenvalues.
2) The matrix is defective. Nonetheless, find the general
solution to the system x’ = Bx. (x is a vector)
a.) Find a basis for the row space of matrix B. b.) Find a basis for the column space of matrix B.
For the given matrix B=
1
1
1
3
2
-2
4
3
-1
6
5
1
a.) Find a basis for the row space of matrix B.
b.) Find a basis for the column space of matrix B.
c.)Find a basis for the null space of matrix B.
d.) Find the rank and nullity of the matrix B.
Consider the following payoff matrix for two firms, Airbus (A) and Boeing (B). The firms can...
Consider the following payoff matrix for two firms, Airbus (A)
and Boeing (B). The firms can each produce either 3 or 4 planes per
week. The table below shows the profit from each of those options.
Each firm knows all the information in the table below. They each
make their decisions independently.
Airbus's Options
4 planes per week
3 planes per week
Boeing's Options
4 planes per week
A = $32 million
B = $32 million
A = $30 million...
1. What is the definition of an eigenvalue and eigenvector of a matrix? 2. Consider the...
1. What is the definition of an eigenvalue and eigenvector of a
matrix?
2. Consider the nonhomogeneous equationy′′(t) +y′(t)−6y(t) =
6e2t.
(a)Find the general solution yh(t)of the corresponding
homogeneous problem.
(b)Find any particular solution yp(t)of the nonhomogeneous
problem using the method of undetermined Coefficients.
c)Find any particular solution yp(t)of the nonhomogeneous
problem using the method of variation of Parameters.
(d) What is the general solution of the differential
equation?
3. Consider the nonhomogeneous equationy′′(t) + 9y(t)
=9cos(3t).
(a)Findt he general...
Let A be an m × n matrix and B be an m × p matrix....
Let A be an m × n matrix and B be an m × p matrix. Let C =[A |
B] be an m×(n + p) matrix.
(a) Show that R(C) = R(A) + R(B), where R(·) denotes the range
of a matrix.
(b) Show that rank(C) = rank(A) + rank(B)−dim(R(A)∩R(B)).
solve for matrix B Let I be Identity matrix (I-2B)-1= 1 -3 3 -2 2 -5...
solve for matrix B
Let I be Identity matrix
(I-2B)-1=
1
-3
3
-2
2
-5
3
-8
9
Consider the 90 degrees rotation matrix R = [0 −1 1 0] a) Are the eigenvalues...
Consider the 90 degrees rotation matrix R = [0 −1 1 0]
a) Are the eigenvalues real?
b) Are the eigenvectors real?
c) Find the determinant of R.
d) Find the trace of R.
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.
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