Question: Suppose that the linear system Ax = b, where A is m ( n, is consistent (i.e., has a solution). Prove that the solution is

Suppose that the linear system Ax = b, where A is m ( n, is consistent (i.e., has a solution). Prove that the solution is unique if and only if rank A = n.

Step by Step Solution

★★★★★

3.37 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose that Ax b is consistent Assume that there ... View full answer

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)

951-M-L-A-L-S (6982).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Find the least squares solution to the linear system Ax = b when a. b. c. d. e. 121 137 015 3 2 -1 A= 1-2 0 , b=10 3 -I 2113 3250 2412 00-0 4132 1202 2115

Let A be an m ( n matrix. Show that the linear system Ax = b has a solution for every m ( 1 matrix b if and only if rank A = m.

Suppose b mg A and kerA = {0}. Prove that x* = A+b is the unique solution to the linear system Ax = b. What if ker A {0}?

X Course Hero Differential Equations and Linear X G Determine all values of the const x M (no subject) - sylviaabdelmasih@ x...

Please answer this using MATLAB. The function being used is in the second picture included. X; = In this exercise, you have to write a function that employs the Cramer's rule to find the solution of...

Please answer this using MATLAB. The function needed is in the second picture. In this exercise, you have to write a function that employs the Cramer's rule to find the solution of a linear system Ax...

9 Suppose that a linear system Ax b has more variables than equations. Show that Ax b cannot have a unique solution.

Let A be a square matrix of order n. The following statements are equivalent. (a) A is invertible. (b) For every vector b E R", the linear system Ax = b has a unique solution. (c) There is a vector b...

Part (a) and (b) have been solved, you only need to solve part (c). You can check the answers of (a) and (b) in the following link:...

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...

Air enters the gas turbine cycle of Fig. 9.44 at 25°C and 100 kPa with a flow rate of 1.2 kg/s. It is compressed so that the temperature at state 2 is 400°C. The temperature entering the...

When the owner of a universal life insurance policy takes a withdrawal from the cash value, there is no tax until the cost basis has been fully recovered: A.TRUE B.FALSE David's employer has...

Which of the following statements is not true about a doubtful allowance account? Group of answer choices amount entered likely ends up as a bad debt expense involves patients who qualify for charity...

Quality assurance is an organization-wide initiative and is part of your enterprise environmental factors. All projects must adhere to the quality assurance initiatives in your company. Within your...

Graph y = - 1 / 4 x + 3 using the slope and the y-intercept.

Clear County Cable Television charges a $110 installation fee and $85 per month for basic service. Write an equation that can be used to determine the total cost C(t) of t months of basic cable...

Find the point on the x-axis that is equidistant from the points (-4, -3) and (-1, 5).

Newton's Method (also know as the Newton-Raphson method, named after Isaac Newton and Joseph Raphson) is an algorithm for finding the root of a nonlinear function, that is, given f(x), this algorithm...

1. A firm had Net Income of $1,000,000 and a payout ratio of 40%. If they are 70% equity financed, how much can they spend on capital expenditures before needing external equity? a) $857,143 b)...

Trans-Atlantic Quotes. Separated by more than 3,000 nautical miles and five time zones, money and foreign exchange markets in both London and New York are very efficient. The following information...