Question: Let A be a nonsingular n n matrix and let B be an n r matrix. Show that the reduced row echelon form

Let A be a nonsingular n × n matrix and let B be an n × r matrix. Show that the reduced row echelon form of (A|B) is (I|C), where C = A-1B.

Step by Step Solution

★★★★★

3.38 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since A is nonsingular it is row equivalent to I Hence there ex... 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

949-M-L-A-E (436).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let A be a nonsingular n n matrix. Use mathematical induction to prove that Am is nonsingular and (Am)-1 = (A-1)m for m = 1, 2, 3, ...

Q:

Let A be a nonsingular n n matrix with n > 1. Show that det(adj A) = (det(A))n-1

Q:

Let A be a nonsingular n n matrix and let be an eigenvalue of A. (a) Show that 0. (b) Show that 1/ is an eigenvalue of A-1.

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:

Complete these simple exercises Math 120 Homework 12: Problem 3 (1 point) Suppose that S, and S, are subspaces of R', with dim(S1) = m, and dim($2) = my. If S, and S, have only 0 in common, then the...

Q:

Matlab help (layout already given) (a-c) (a) Use the reduced row echelon form (RREF) to solve Ax = b, where A and b are indicated in Exercise 1, and type your answer for the following in the Live...

Q:

Use the reduced row echelon form ( RREF ) to solve Ax = b , where A and b are indicated in Exercise 1 , and type your answer for the following in the Live Editor. Display the reduced row echelon form...

Q:

The command rref ( is ) returns the reduced row echelon form of a matrix A 1 The command , pivcols ] = rref ( A ) returns B and pivcols, where matrix B = rref ( A ) and pivcols indicates pivot...

Q:

l. [3 marks for each part) Solve each system of linear equations {over R]. Use Gauss-Jordan elimination {matrix row reduction). [at] {6] :r 23; 32 l 4:: 53; 62 l in: 83; +102 = l to +21 2y +3z = 2 2w...

Q:

Exercise 2 -- solving Ax = b (30 points; 10 points per part) In this exercise, you use RREF and Rouch-Capelli Theorem to determine if Ax = b is consistent. You may need the following commands for...

Q:

During 2011, Magma Company changed its inventory valuation method from LIFO to FIFO. The following information shows the effect of this change. Instructions: 1. Before the change from LIFO to FIFO,...

Q:

The ROAR company manufactures a single product that sells for $17.00 each. The cost of each unit produced at a monthly production level of 10,000 units is: Direct materials $2.75 Direct labour $3.25...

Q:

Name and discuss the four basic methods of pricing intracompany transfers.

Q:

When the project was begun, both the customer and the project manager understood that it was likely that some service scope changes would occur. A few weeks into the project, some services need to be...

Q:

(a) Use the results in Exercise 14 to construct a formula for the determinant of a 4 Ã 4 matrix. (b) Why do the mnemonics of Figure 2.4.2 fail for a 4 Ã 4 matrix? 14 a2 %)

Q:

Use the combinatorial definition of the determinant to evaluate (a) (b) 30000 04000 00100 00020 00005 04000 00010 00300 00002 50000

Q:

Show that the value of the determinant does not depend on θ, using the method of this section. Sin -cos sin _ cos cos8 0 sin + cos 1

Q:

Can someone help me solve this? You are considering on investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Joumal reports that 1-year T-bills...

Q:

1) You have started your first job today, and you want to buy a house within 3 years. You are currently saving for the down payment. You plan to save $5,000 the first year. You also anticipate that...

Q:

---Can you please help me on 8c and all parts of number 9? I have A and B on number 8. Thank you! 8. (9 points possible) Suppose your company needs to raise $10 million to construct a new office...