Let S be an m n matrix and let b Rm. Show that b

Question:

Let S be an m × n matrix and let b ∈ Rm. Show that b ∈ R(A) if and only if
b =AA+b

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 01:07 AM

See More Questions

Let A be an m n matrix and let c be a scalar. Show that if c A =0, then either c = 0 or A = O.
Let A be an m n matrix and c be a nonzero vector in n. Then exactly one of the following systems has a nonnegative solution: Either I Ax 0 and cx > 0 for some x Rn+ or II ATy c for some y Rm+....
Let A be an m n matrix and c be a nonzero vector in n. Then exactly one of the following systems has a solution: Either I Ax = 0 and cx > 0 or II ATy = c
Freddie and Jason have just opened the Texas Toothpick, a chain-saw sharpening and repair service located on Elm Street. The Texas Toothpick promises same-week repair service. Freddie and Jason are...
The series of seven transactions recorded in the following T accounts were related to a sale to a customer on account and the receipt of the amount owed. Briefly describe eachtransaction. Cash Notes...
Spains economy has struggled with very high unemployment rates as a result of the Eurozone banking crisis. The following data show the annual unemployment rate over a nine year period. These data can...
A six-cylinder, 4-stroke SI engine delivers $400 \mathrm{~kW}$ at $2200 \mathrm{rpm}$. Determine the bore and stroke from the following data : Compression ratio $=7.6 ;$ stroke to bore ratio...
The Italian Bread Company purchased land as a factory site for $ 70,000. An old building on the property was demolished, and construction began on a new building. Costs incurred during the first year...
Tarrant Amertex Regional Hospital, one of our hospitals in the Fort Worth area, has been in need of a new Chief Executive Officer. Last week, we reached a "handshake" dealthough per current protocols...
A scale is constructed using the 10-kg mass, the 2-kg pan P, and the pulley and cord arrangement. Cord BCA is 2 m long. If s = 0.75 m, determine the mass D in the pan. Neglect the size of thepulley....
Show that if A is a m n matrix of rank n then A+ = (ATA)-1AT
If a, b, and c are floating - point numbers, then fl(fl(a + b) + c) = fl(a + fl(b + c)) In the case of a true statement, explain or prove your answer. In the case of a false statement, give an...
Tyler Richardson set up a house alarm system when he moved to his new home in Seattle. For security purposes, he has all of his mail, including his alarm system bill, mailed to his local UPS store....
How do concepts of deviance intersect with broader themes of power, hegemony, and social hierarchy in contemporary society ?
-What is the typical craft brewer's strategy? -Why would a craft brewer go international? -What is Beau's strategy? -Which (internationalization) option "fits" best with Beau's strategy? What...
In the following C function, let n > m. int gcd(n,m){ if (n%m 0) return m; n = n%m; return gcd(m, n); } How many recursive calls are made by this function?
On June 3, 2010, a fire broke out in Heidi Heise's Dartmouth, N.S., apartment building. Several tenants had to find other accommodations, but fortunately Heidi's apartment was not damaged and she did...
How do sociological theories of deviance account for variations in deviant behavior based on factors like gender, race, and socioeconomic status ?
Find a real general solution of the following systems. Show the details. y' 1 = 2y 1 + 5y 2 y' 2 = 5y 1 + 12.5y 2
Write a paper about medication error system 2016.
Determine the singular value decomposition of 4 122
Determine the singular value decomposition of 1101 0111 1110
An m ( n matrix A is said to have full rank if rank A = minimum [m, n]. The singular value decomposition lets us measure how close A is to not having full rank. If any singular value is zero, then A...
Question Content Area Changes in current operating assets and liabilities indirect method Victor Corporation's comparative balance sheet for current assets and liabilities was as follows: Line Item...
Determine a value of m (if possible) for which f is continuous at x = 1. mx-3 if x <1 f(x)= 3x if x1
Z Find zw and z=8-8i w= 3+i Write each answer in polar form and in exponential form. The product zw in polar form is and in exponential form is (Simplify your answer. Type an exact answer, using it...

Let S be an m n matrix and let b Rm. Show that b

Question:

Step by Step Answer:

Let b AA b AA b since RA Ax x 2 ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions