Plese help me!!!(Conditioning of Problems and
Stability of Algorithms)
Homework Answers
Add Answer to:
Plese help me!!!(Conditioning of Problems and Stability of Algorithms) IA is an m x n matrix, and x is an n x 1 vector,...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
10.10 If A is an 'n x n matrix, and x is an n x 1 vector, then the linear transformation y = Ar maps* n to·m, so th...
10.10 If A is an 'n x n matrix, and x is an n x 1 vector, then the linear transformation y = Ar maps* n to·m, so the linear transformation should have a condition number, condAx (x). Assume that l a subordinate norm a. Show that we can define condar (x)-[All Irl/IArll for every x 0. b. Find the condition number of the linear transformation atx [ - 2 using the oo-norm ng the oo-norm. T-3 2 1 .12...
12. a. If there is an n x n matrix D such that AD = 1,...
12. a. If there is an n x n matrix D such that AD = 1, then there is also an n x n matrix C such that CA= 1. b. If the columns of A are linearly independent, then the columns of A span Rn. c. If the equation Ax = b has at least one solution for each bin Rn, then the solution is unique for each b. d. If the linear transformation (x) -> Ax maps Rn into Rn, then...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0,...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
A.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero mat...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
Let A be an m x n matrix of unspecified rank. Let b e Rm, and let Prove that this infimum is atta...
Let A be an m x n matrix of unspecified rank. Let b e Rm, and let Prove that this infimum is attained. In other words, prove the existence of an ax for which l|Ax bll p. In this problem, the norm is an arbitrary one defined on Rm.
Let A be an m x n matrix of unspecified rank. Let b e Rm, and let Prove that this infimum is attained. In other words, prove the existence of an...
3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL ...
3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL we have |lU 2 2. Thus the 2-norm of a vector does not change when it is multiplied by an orthogonal matrix.
3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL we have |lU 2 2. Thus the 2-norm of a vector does not change...
4. Consider solving the linear system Ax = b, where A is an rn x n matrix with m < n (under- determined case), b...
4. Consider solving the linear system Ax = b, where A is an rn x n matrix with m < n (under- determined case), by minimizing lle subject to Ar-b. (a) Show that if A Rmxn is full (row) rank, where m n, then AA is invertible. Then show that r.-A7(AAT)-ibis a solution to Ax = b. (b) Along with part (a) and the solution aAT(AA)-b, show that l thus, z is the optimal solution to the minimization problem. and...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equa...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
10.10 If A is an 'n x n matrix, and x is an n x 1 vector, then the linear transformation y = Ar maps* n to·m, so the linear transformation should have a condition number, condAx (x). Assume that l a subordinate norm a. Show that we can define condar (x)-[All Irl/IArll for every x 0. b. Find the condition number of the linear transformation atx [ - 2 using the oo-norm ng the oo-norm. T-3 2 1 .12...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
Let A be an m x n matrix of unspecified rank. Let b e Rm, and let Prove that this infimum is attained. In other words, prove the existence of an ax for which l|Ax bll p. In this problem, the norm is an arbitrary one defined on Rm.
Let A be an m x n matrix of unspecified rank. Let b e Rm, and let Prove that this infimum is attained. In other words, prove the existence of an...
3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL we have |lU 2 2. Thus the 2-norm of a vector does not change when it is multiplied by an orthogonal matrix.
3. Let U E Rnxn be an orthogonal matrix, i.c., UTU = UUT-1. Show that for any vector x E Rn LXTL we have |lU 2 2. Thus the 2-norm of a vector does not change...
4. Consider solving the linear system Ax = b, where A is an rn x n matrix with m < n (under- determined case), by minimizing lle subject to Ar-b. (a) Show that if A Rmxn is full (row) rank, where m n, then AA is invertible. Then show that r.-A7(AAT)-ibis a solution to Ax = b. (b) Along with part (a) and the solution aAT(AA)-b, show that l thus, z is the optimal solution to the minimization problem. and...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
Most questions answered within 3 hours.
-
Describe how the file manager allocates a file to a single user.
List the steps that...
asked 4 minutes ago -
For the following reaction:
IBr(g) + 4F2(g) → IF5(g) +
BrF3(g)
Compound
ΔH°f (kJ mol-1)...
asked 5 minutes ago -
Assuming the simple probability of even A is given as P(A) and
the simple probability of...
asked 8 minutes ago -
2.- It is known that 20% of the students on campus are smokers.
If 8 students...
asked 8 minutes ago -
Provide a summary/reflection of what you gleaned of how law
enforcement is effect by Unconventional Weapons...
asked 29 minutes ago -
From the following heats of combustion,
CH3OH(l) + 3/2O2(g) → CO2(g) +
2H2O(l)
ΔHorxn = –726.4...
asked 23 minutes ago -
Floating Point Representation
Consider a computer that stores information using 10 bits words.
The first bit...
asked 52 minutes ago -
. The theoretical weight percent of carbon in (CH3)3N is:
A. 20.32% B. 81.95% C. 9.97%...
asked 45 minutes ago -
The rate of a certain reaction is given by the following rate
law:
rate = k[H2][I2]...
asked 39 minutes ago -
A 10,000 uF capacitor is in series with a 1 uH inductor. What is
Zeq of...
asked 44 minutes ago -
Draw the molecular orbital diagram for O2-
(oxygen molecule with a negative charge).
asked 1 hour ago -
Of all the different weapons discussed in this chapter that make
up CBRNE,
Which group do...
asked 58 minutes ago