Question

For the linear system Ax = b, with A and b defined as A= [1 2...

For the linear system Ax = b, with A and b defined as

A= [1 2 -1; 2 3 1; -1 -1 -2; 3 5 0]

B= [1; 0; 1; 0]

(a) By hand, calculate the pseudoinverse A+

(b) Use the pseudoinverse to calculate a least squares solution for the

system.

(c) Calculate the least squares solution to the system in MATLAB,

using mldivide (i.e., A\b).

(d) Calculate the size of the error e from each solution, and compare the size of each least squares solution xˆ. How do the errors and sizes compare?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

(a)

(b)

(c)

define A and B as shown in question. then use the mldivide function as shown below:

(d)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A linear system of equations Ax=b is known, where A is a matrix of m by...
A linear system of equations Ax=b is known, where A is a matrix of m by n size, and the column vectors of A are linearly independent of each other. Please answer the following questions based on this assumption, please explain it, thank you~. (1) To give an example, Ax=b is the only solution. (2) According to the previous question, what kind of inference can be made to the size of A at this time? (What is the size of...
4. Suppose that we have a linear system given in matrix form as Ax = b,...
4. Suppose that we have a linear system given in matrix form as Ax = b, where A is an m×n matrix, b is an m×1 column vector, and x is an n×1 column vector. Suppose also that the n × 1 vector u is a solution to this linear system. Answer parts a. and b. below. a. Suppose that the n × 1 vector h is a solution to the homogeneous linear system Ax=0. Showthenthatthevectory=u+hisasolutiontoAx=b. b. Now, suppose that...
Exercise 2.4 Assume that a system Ax = b of linear equations has at least two...
Exercise 2.4 Assume that a system Ax = b of linear equations has at least two distinct solutions y and z. a. Show that xk = y+k(y−z) is a solution for every k. b. Show that xk = xm implies k = m. [Hint: See Example 2.1.7.] c. Deduce that Ax = b has infinitely many solutions.
Suppose Ax = b 0 is a linear system and A is a square, singular matrix....
Suppose Ax = b 0 is a linear system and A is a square, singular matrix. How many solutions is it possible for the system to have?
x1-5x2+x3+3x4=1 2x1-x2-3x3-x4=3 -3x1-3x3+7x3+5x4=k 1 ) There is exactly one real number k for which the system...
x1-5x2+x3+3x4=1 2x1-x2-3x3-x4=3 -3x1-3x3+7x3+5x4=k 1 ) There is exactly one real number k for which the system has at least one solution; determine this k and describe all solutions to the resulting system. 2 ) Do the solutions you found in the previous part form a linear subspace of R4? 3 ) Recall that a least squares solution to the system of equations Ax = b is a vector x minimizing the length |Ax=b| suppose that {x1,x2,x3,x4} = {2,1,1,1} is a...
Is the solution set of a non-homogeneous linear system "Ax=b" a subspace? Give reason(s) to support...
Is the solution set of a non-homogeneous linear system "Ax=b" a subspace? Give reason(s) to support your answer
y[n] =b(ax[n] +x[n-1]+ax[n-2]) where a&b >0. Find the frequency response of the system H(e^jw). Determine the...
y[n] =b(ax[n] +x[n-1]+ax[n-2]) where a&b >0. Find the frequency response of the system H(e^jw). Determine the values of a & b, if the magnitude response of the filter at w = 0 is 1 and at w =pi÷2 is 0.5. thanks
Find LU factorization of A.solve the system Ax=b using LU fact A=(1 -3 0, 0 1...
Find LU factorization of A.solve the system Ax=b using LU fact A=(1 -3 0, 0 1 -3,2 -10 2). b=(-5,-1,-20)
Given a matrix system AX = B as below, where A is a 4 x 4...
Given a matrix system AX = B as below, where A is a 4 x 4 matrix as given below A: 2          1          0          0 1          2          1          0 0          2          4          1 0          0          1          3 B: 0         -1 3 -1 Solve for all 4 X values using TDMA algorithm First identify the a, d, c and b values for each row, and then find P’s and Q’s and finally determine X’s.
1. You are given the following data to fit a simple linear regression x 1 2...
1. You are given the following data to fit a simple linear regression x 1 2 3 4 5 y -2 4 2 -1 0 Using linear least squares, determine the t-value for testing the hypothesis that no linear relationship exist between y and x. (a) 0.01, (b) 0.03, (c) 0.09, (d) 0.11, (e) 0.13
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT