Suppose A is an m n matrix. (a) Let v1,..., vn be a basis of Rn,
Question:
(a) Let v1,..., vn be a basis of Rn, and Av1 = w1 ∈ Rm, for i = 1........n. Prove that the vectors v1,..., vn, w1,..., wn, serve to uniquely specify A.
(b) Write down a formula for A.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (7 reviews)
a Given any v R n write v c 1 v 1 c n v n then Av c 1 ...View the full answer
Answered By
Ajeet Singh
Hi there! Are you looking for a committed, reliable, and enthusiastic tutor? Well, teaching and learning are more of a second nature to me, having been raised by parents who are both teachers. I have done plenty of studying and lots of learning on many exciting and challenging topics. All these experiences have influenced my decision to take on the teaching role in various capacities. As a tutor, I am looking forward to getting to understand your needs and helping you achieve your academic goals. I'm highly flexible and contactable. I am available to work on short notice since I only prefer to work with very small and select groups of students. Areas of interest: Business, accounting, Project management, sociology, technology, computers, English, linguistics, media, philosophy, political science, statistics, data science, Excel, psychology, art, history, health education, gender studies, cultural studies, ethics, religion. I am also decent with math(s) & Programming. If you have a project you think I can take on, please feel welcome to invite me, and I'm going to check it out!
5.00+
4+ Reviews
24+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Suppose A is an m ( n matrix with the property that for all b in the equation Ax = b has at most one solution. Use the definition of linear independence to explain why the columns of A must be...
-
Let [v1, v2,...,vn} be a basis of Rn (written as columns), and let A be an n n matrix. If {Av1, Av2,..., Ayn} is a basis of Rn, show that A is invertible.
-
Suppose that A is an m n matrix A. Show that Rank(A) is the same as the Rank(At).
-
A wooden bookshelf has external dimensions as follows :Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished...
-
Why should a global marketing manager consult local attorneys in other countries before creating a marketing campaign? Since the end of World War II, international trade in goods and services has...
-
A recent GSS reported that the 486 surveyed females had a mean of 8.3 close friends (s = 15.6) and the 354 surveyed males had a mean of 8.9 close friends (s = 15.5). a. Estimate the difference...
-
The mean wages for a sample of employees in a company was \($18.00\) per day with a standard deviation of \($2.50\) per day. Between what two values do 95% of the data lie? (Assume the data set has a...
-
Upon starting your new job after college, you've been confronted with selecting the investments for your 401(k) retirement plan. You have four choices for investing your money: A money market fund...
-
Wardell Company purchased a minicomputer on January 1, 2022, at a cost of $57,000. The computer was depreciated using the straight-line method over an estimated five-year life with an estimated...
-
When Timmy was 18 months old, his mother stood behind him, helping him throw a large ball into a box. As his skill improved, she stepped back, letting him try on his own. Using Vygotsky's ideas,...
-
(a) Show that every invertible linear function L: Rn Rn can be represented by the identity matrix by choosing appropriate (and not necessarily the same) bases on the domain and target spaces. (b)...
-
Suppose a linear transformation L: Rn Rn is represented by a symmetric matrix with respect to the standard basis e1,..., en. (a) Prove that its matrix representative with respect to any orthonormal...
-
What kind of polymer can be used to line the inside of the head of a hip prosthesis implant? Discuss what requirements would be needed for this type of polymer.
-
Is it possible in the simple model of exchange or in the static Arrow-Hurwicz model that an allocation not accepted by traders is Pareto optimal?
-
What conditions need to be satisfied by exogenous linear: demand function and function of product supply to have a positive equilibrium price established on a market of this product?
-
In periods price of the first good and the price of the second good change according to equations: t = 0, 1, 2, ..., 20 a utility level a consumer wants to achieve, the
-
What is the Edgeworth box used for in the simple model of exchange and in the static Arrow-Hurwicz model?
-
What does it mean that the Wairasian equilibrium price vector is determined to accuracy of a structure (multiplication by a positive number)? What does it result from? What does it result in?
-
For the following exercises, rewrite in terms of sin x and cos x. sin (x + 11/6)
-
What exactly is a prima facie duty? How does an ethic of prima facie duties differ from monistic and absolutist ethical theories?
-
Rework Exercise 8-27 to compute a 95% lower confidence bound on rod diameter. Compare this bound with the lower limit of the two-sided confidence limit from Exercise 8-27. Discuss why they are...
-
The wall thickness of 25 glass 2-liter bottles was measured by a quality-control engineer. The sample mean was x = 4.05 millimeters, and the sample standard deviation was s = 0.08 millimeter. Find a...
-
An article in Nuclear Engineering International (February 1988, p. 33) describes several characteristics of fuel rods used in a reactor owned by an electric utility in Norway. Measurements on the...
-
4. A stock provides a dividend yield of 5.0% paid semi- annually. The spot price of the stock is currently $500, and the risk-free rate is 7.5% with continuous compounding for all maturities. 1. What...
-
1. A 1000 bond issued on January 10, 2021 is paying coupons at a nominal interest rate of 7% payable semiannually. The bond is redeemed at par and matures on January 10, 2031. The nominal yield rate...
-
Ruzgar Inc., bonds were selling at $1,040 a year ago. A friend of yours invested into this bond and just received a $100 coupon payment. She sold the bond today for $1,200.If the inflation rate for...
Study smarter with the SolutionInn App