Question: Prove that any linear system with a nonsingular matrix of coefficients has a solution, and that the solution is unique.

Prove that any linear system with a nonsingular matrix of coefficients has a solution, and that the solution is unique.

Step by Step Solution

★★★★★

3.42 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Because the matrix of coefficients is nonsingular Gausss Method ends with an echelon form where ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

961-M-L-A-L-S (5080).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Say as much as possible about each system's solution set. Be sure to make it clear which theorems you are using to reach your conclusions. 1. 6 equations in 6 variables, singular coefficient matrix....

Q:

(a) Prove that for any linear map h: V W and any W, the set h-1() has the form { + | N (h)} for V with h() = (if h is not onto then this set may be empty). Such a set is a coset of N (h) and we...

Q:

Prove that a linear system has a solution if and only if that system's matrix of coefficients has the same rank as its augmented matrix.

Q:

Purpose: The purpose of this lab is for you to learn how to use a computer to solve problems dealing with systems of equations. In future classes and when you are working in industry, linear algebra...

Q:

Python the echelon had been asked before, but the code doesnt work out. Part B: General Forward Elimination In the lecture we assumed that the input matrix to Gaussian Elimination is non-singular"....

Q:

An m n matrix has full row rank if its row rank is m, and it has full column rank if its column rank is n. (a) Show that a matrix can have both full row rank and full column rank only if it is...

Q:

1. (4 Points) Let x and y be vectors in R". None of the given choices. O If [x) + lyl = [x + yl. then x and y are parallel. If x . y = 1, then x and y are parallel. O If [x x yl = 1, then x and y are...

Q:

6. Consider the Arnoldi procedure or the Lanczos procedure. Suppose that the matrix A is nonsingular. Show that once the breakdown occurs, the solution to the linear system AT = 5 lies in Kk+1, and...

Q:

(4) 5. Fill in the blanks. The missing word is must (always true), might (sometimes true and sometimes false) or cannot (always false). (a) An underdetermined linear system have a unique solution....

Q:

I need help with this question and do it carefully so that i can understand it. 13. Use Gauss-Jordan elimination to solve the given system of linear equations T" 14. For what value of k, if any, will...

Q:

Vista Landscaping uses a job-order costing system to track the costs of its landscaping projects. The company provides garden design and installation services for its clients. The table below...

Q:

Which of the following is correct? a. The manual ruling method can be used to correct an error in the ledger after an entry has been posted. b. The correcting entry method can only be completed in...

Q:

Which option is an example of a cash flow from operating activities? Solution A.Cash payments to acquire property, plant and equipment, intangibles, and other long-term assets. B.Cash receipts from...

Q:

[Related to the Making the Connection on page 300] An Associated Press article about sticky prices states: Thats what analysts call it when companies slap higher prices on products and keep them...

Q:

In Exercises 1 and 2, find the line of intersection of the given planes. 1. 3x + 2y + z = - 1 and 2x - y + 4z = 5 2. 4x + y + z = 0 and 2x - y + 3z = 2

Q:

(a) Give an example of three planes that have a common line of intersection (Figure 2.4). Figure 2.4 (b) Give an example of three planes that intersect in pairs but have no common point of...

Q:

In Exercises 1 and 2, determine whether the lines x = p + su and x = q + tv intersect and, if they do, find their point of intersection. 1. 2. 110 220 101 310

Q:

On November 14, Thorogood Enterprises announced that the public and acrimonious battle with its current CEO had been resolved. Under the terms of the deal, the CEO would step down from his position...

Q:

MCentral Heating Co. is considering a project with the following financial characteristics: Fixed capital outlay is $1.5 billion Investment in net working capital is $0.4 billion. Straight-line...

Q:

Compare the natural uranium fuel needs in the case of the PWR design to the CANDU design.