Find the projection matrix

Assignment Help Algebra
Reference no: EM131276663

1. Given


1 2 5 4
A =  1 3 6 3

2 4 10 8

Find each of the following:

Solvability condition

Particular solution for


1
b = 2

2

Complete solution

2. Choose a vector in each of the fundamental spaces of A. Prove that your choice lives in the space the use these to verify the following.

∀b ∈ C(A) ⊥ ∀y ∈ N(AT)

and

∀r ∈ C(AT) ⊥ ∀x ∈ N(A)

3. Identify the independent columns of A. Use the definition of linear independence to prove that the independent columns of A are linearly independent.

4. In the vector space P3 of all p (x) = a0 + a1x + a2x2 + a3x3, let S = {p(x)|p(x)∈P3,p'(0)= 0]. Verify that S is a subspace.

5. Determine if T(v) v except that T(0, v2) = (0,0) is a linear transformation.

6. Prove that two nonzero orthogonal vectors in R2 are linearly independent.

7. What multiple of


1
A =  1

1

is closest to the point b =


1
b = 2

2

8. Find the projection matrix P that projects b onto the line through a.

Verified Expert

paper was combination of Matrix and vectors. Both are inter related. Vectors are very useful in day to day life including mentioning and solving many scientific problems. As vectors show the direction and value of particular object or physical quantity. But sometimes vectors can be complicated in presentation and in description. To find out what will be the output of so many vectors in multi-dimensional space we need the help of Matrices. As properties of Matrices help us to represent or to get the output out of so many vectors to find out the certain properties of vectors. These methods are often used in gaming or designing where certain points of certain objects represent certain vectors regarding reference object and in certain condition how they will react or change that can be sort out by using matrices by filling up these vectors in them.

Reference no: EM131276663

Questions Cloud

Locate a long term recovery plan : Locate a long-term recovery plan that was developed to manage the coordination of recovery efforts following a disaster in the United States.
What would object b need to weigh on earth : Two objects have exactly the same mass. If object A weighs 300N on the Moon what would Object B need to weigh on Earth?
Find the maximum temperature in the cycle : Determine the second-law efficiency of the cycle and the rate of energy output with the exhaust gases when they are purged.
What are the implications of the paradox for the application : The textbook claims that standards are both necessary and dispensable. What does that mean? What are the implications of this paradox for the application of corporate responsibility standards?
Find the projection matrix : Identify the independent columns of A. Use the definition of linear independence to prove that the independent columns of A are linearly independent - Find the projection matrix
What was the average effect of the process change : What was the average effect of the process change? Did the process average increase or decrease and by how much? How does this model measure the effect of the process change?
How should the decision-making process be handled : How should the decision-making process be handled. How should the intrinsic as well as the instrumental value of a human life be determined?
Calculate the network output per unit mass : Calculate the network output per unit mass.
How should the decision-making process be handled : How should the decision-making process be handled. How should the intrinsic as well as the instrumental value of a human life be determined?

Reviews

Write a Review

Algebra Questions & Answers

  Addressing inequality in education

Savage Inequalities is a wonderful book to reference here as it does point to the problem of inequitable funding. In other words the poor stay poor because the school is funded disproportionally from community to community.

  How many roots does x^2-2 have modulo 8

Describe the maximal ideal of RxR where in this case R is the set of real numbers;

  Find an expression for the kinetic energy e of the particle

Find an expression for the kinetic energy E of the particle, given in terms of its mass m and its speed v by E = 0.5mv^2.

  Polynomial functions and validity

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counter example.

  Solve the given equation

Solve the given equation.

  Are the given equations are dependent or independent

Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

  Compounding inequality

Juanita had a job offer to be an automobile sales position that pays $1500 per month plus 2.5% of all sales. What total sales is required to earn between $4000 and $6000 per month?

  Nepper miliampers conversion

The attenuation constant of a transmission line, measured in nepers, is defined as the natural logarithm of the ratio of the input current to the line to the output current from the line.

  Compute the width & length of the cattle yard

Compute the width & length of the cattle yard.

  What is the smallest cube integer of the form n to the

what is the smallest cube integer of the form n to the third that is divisible by 16 but is not a square number b to

  Homomorphism image

Homomorphism image.

  Identify the real and imaginary parts

Identify the real and imaginary parts for each expression and Rationalize the denominator - Add or subtract as indicated. Assume all variables represent positive real numbers

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd