How do the dimensions of the nullspace and column space of a matrix relate to the number

Question:

How do the dimensions of the nullspace and column space of a matrix relate to the number of lead and free variables in the reduced row echelon form of the matrix? Explain.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:52 AM

See More Questions

Let A be an m n matrix with m > n. Let b Rm and suppose that N(A) = {0}. (a) What can you conclude about the column vectors of A? Are they linearly independent? Do they span Rm? Explain. (b) How...
Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) ||u + v + w|| ||u|| + ||v|| + ||w|| for all vectors u, v,...
In each case, show that the reduced row-echelon form is as given. (a) (b) 1 0 0 b0 0 with abe0 0 0 00 1 1 a c 10 (-1 c a+b
Read the article Problem at INSPEECH and answer the question: Why did Inspeech experience a meltdown in 1988?
Why do banks not eliminate the need for money markets?
Evaluate Belbins model of team roles. Which three or four roles are of most importance in an effective team? What is your preferred role?
2. Do you think that this hedge would be considered effective and therefore would qualify for hedge accounting?
GigaCo. manufactures 1-GB flash drives (jump drives). Price and cost data for a relevant range extending to 200,000 units per month are as follows: Sales price per unit (current monthly sales volume...
7. During the Christmas season, Holiday offers a special to its retail customers. Customers can send in 4 UPC codes from boxes of Christmas lights along with $3.25 and receive one box of Christmas...
Read the given description of a CSP and write solution as per the given questions: [20] YCPS@GIFT is going to arrange a gaming competition at campus. They are considering using seven games for this...
Given (a) Find a basis for N(A) (the null space of A). What is the dimension of N(A)? (b) Find a basis for the column space of A. What is the rank of A? 4123 3123 1123 3000 1000
Answer the following questions and in each case give geometric explanations of your answers. (a) Is it possible to have a pair of one dimensional subspaces U1 and U2 of R3 such that U1 U2 = {0}? (b)...
Perfect Products Co. applied for a substantial bank loan from Capitol City Bank. In connection with its application. Perfect engaged William & Co., CPAs, to audit its financial statements. William...
a) Discuss whether bike paths can be considered a public good. Now consider a hypothetical town. Suppose that there are three equal-size groups in the economy with the following demand curves: Group...
Event services and management can be a lucrative revenue generator. What are the two most important factors in developing a successful event service and management business, whether it is independent...
Show how the buying process occurs in the consumer. Review some of the steps in the buying process, stories like: felt need pre-purchase activity purchase decision Post-purchase feelings Explain and...
How did Henry Ford set the stage for some of the same problems we still face today in employee relations, especially in manufacturing? 2) If you were a human resources manager, how would you address...
What does a DMO risk by not having a positioning theme? Critique the potential of your destination's slogan to effectively differentiate against rivals. you have been asked by a television network to...
When a reaction is exothermic, is the sum of bond energies of products or of reactants greater?
Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...
The trace of a square matrix A, denoted tr A, is the sum of the elements on the main diagonal of A. Show that, if A and B are n n matrices: (a) tr(kA) = k tr(A) for any number k. (b) tr(AAT) is the...
A square matrix P is called an idempotent if P2 = P. Show that: If P is an idempotent, so is Q = P + AP - PAP for any square matrix A (of the same size as P).
If A and B are n n matrices, show that: (a) AB = BA if and only if (A + B)2 = A2 + 2AB + B2. (b) AB = BA if and only if (A + B)(A - B) = (A - B)(A + B).
Q1) The equity of Washington Ltd at 1 July 2020 consisted of: Share capital 500 000 A ordinary shares fully paid $1 500 000 400 000 B ordinary shares issued for $2 and paid to $1.50 600 000 General...
out The following information relates to Questions 1 to 2. The management accountant of a furniture manufacturer is developing a standard for the labour cost of one massage chair. When operating at...
Exercise 10-8 Utilization of a constrained Resource [LO10-5, L010-6] Barlow Company manufactures three products: A, B, and C. The selling price, variable costs, and contribution margin for one unit...

How do the dimensions of the nullspace and column space of a matrix relate to the number

Question:

Step by Step Answer:

The columns of the matrix that correspond to the lead variables are linearly independent and spa...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions