Let A be an in x n matrix and let V be a subspace of R. (a)
Question:
(a) Show that W = AV = { A v | v € V } forms a subspace of rng A.
(b) If dim V = k, show that dim W ≤ min{k, r}, where r = rank A.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 53% (15 reviews)
a First W rng A since every w W can be written as w Av for ...View the full answer
Answered By
Fahmin Arakkal
Tutoring and Contributing expert question and answers to teachers and students.
Primarily oversees the Heat and Mass Transfer contents presented on websites and blogs.
Responsible for Creating, Editing, Updating all contents related Chemical Engineering in
latex language
4.40+
8+ Reviews
22+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Let A be an n x n matrix and let A he a nonzero elgenvalue of A. Show that if x is an eigene.1or belonging to A, then x is in the column space of A. Hence the eigenspace corresxponding to is a...
-
Let A be an n x n matrix and let A be an eigenvalue of A whose eigenspace has dimension k. where I where I is the k x k identity mairk. (b) Use Theorem 6.1.1 to show that is an eigenaIue of A with...
-
Let A be an n x n matrix and let || ||M be a matrix norm that is compatible with some vector norm on Rn. If is an eigenvalue of A, show that | | ||A||M.
-
You deposit $12,000 annually into a life insurance fund for the next 10 years, at which time you plan to retire. Instead of a lump sum, you wish to receive annuities for the next 20 years. What is...
-
How would you define project success? Include both the objective and subjective criteria
-
Vargas, Inc., produces industrial machinery. Vargas has a machining department and a group of direct laborers called machinists. Each machinist is paid $25,000 and can machine up to 500 units per...
-
Describe the measurements that would have to be taken and the equations that would have to be used to determine \(G_{23}, v_{32}\), and \(E_{2}\) for a specially orthotropic, transversely isotropic...
-
The Bigco pension plan has invested in dozens of VC funds. The director of the pension plan is preparing his annual report to the Bigco board of directors. Summary information for Bigcos VC portfolio...
-
Ron Marden and Tip Baker operate separate auto repair shops. On January 1, 2020, they decide to combine their separate businesses which were operated as proprietorships to form M & B Auto Repair, a...
-
To study the rate of growth of population in Belize over the period 19701992, Mukherjee et al. estimated the following models: where Pop = population in millions, t = trend variable, D t = 1 for...
-
(a) Suppose A.B are m x n matrices such that ker A = ker B. Prove that there is a nonsingular m m matrix M such that MA = B. (b) Use this to conclude that if Ax = b and Bx = c have the same...
-
(a) Show that an m n matrix has a left inverse if and only if it has rank n. (b) Show that it has a right inverse if and only if it has rank m. (c) Conclude that only nonsingular square matrices...
-
A sample of 18K gold contains the following by mass: 18.0 grams gold, 3.0 grams silver, and 3.0 grams copper. What is the percent gold? (a) 18% (b) 25% (c) 33% (d) 75% (e) 90%.
-
Contrast SCM systems with ERP systems. Which do you suspect are larger and more costly?
-
How might the concept of a facilitating good alter the way we perceive a product? A service?
-
Kyra buys an iPhone for $240 and gets consumer surplus of $160. a. What is her willingness to pay? b. If she had bought the iPhone on sale for $180, what would her consumer surplus have been? c. If...
-
What appears to be the primary secret of successful supply chain management?
-
Outline the four-stage process of change in the audit expectationperformance gap identified as an outcome of reviewing changes in the gap in New Zealand and the UK between 1989 and 2008.
-
a. Plot g m versus V GS for an n -channel JFET with I DSS = 12 mA and V P = -6 V. b. Plot g m versus I D for the same n -channel JFET as part (a).
-
14. In testing the existence assertion, an auditor ordinarily works from the a. Financial statements to the accounting records. b. General journal to the general ledger. c. Supporting evidence to the...
-
For each f C[0. 1] define L,(f) = F, where Show that L is a linear operator on C[0, 1] and then find L(ex) and L(x2). F(x) = f(t)dt 0 x 1
-
If L is a linear transformation from V to IV, use mathematical induction to prove that L(a1v1 + a2v2 +...... + anvn) = a1L(V2) + a2L(v2) +.......+ anL(vn)
-
Let (v1,...,vn) be a basis for a vector space V, and let L1 and L2 be two linear transformations mapping V into a vector space W. Show that if L1(v1) = L2(v1) for each i = I,... ,11 then L1 = L2...
-
s Machine-hours required to support estimated production Fixed manufacturing overhead cost Variable manufacturing overhead cost per machine-hour Required: 1. Compute the plantwide predetermined...
-
How do visionary leaders navigate the complexities of organizational dynamics to cultivate a culture of innovation and adaptability ? Explain
-
Finnish Corporation manufactures custom molds for use in the extrusion industry. The company allocates manufacturing overhead based on machine hours. Selected data for costs incurred for Job 532 are...
Study smarter with the SolutionInn App