Suppose that f: V W preserves structure. Show that f is one-to-one if and only if

Question:

Suppose that f: V → W preserves structure. Show that f is one-to-one if and only if the unique member of V mapped by f to W is V.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 01:59 AM

See More Questions

Suppose that f. V W is an isomorphism. Prove that the set {1, . . . , k} V is linearly dependent if and only if the set of images {f(1), . . . , f(k)} W is linearly dependent.
Where f: V W is linear, suppose that f(1) = 1, . . . , f(n) = n for some vectors 1, . . . , n from W. (a) If the set of 's is independent, must the set of 's also be independent? (b) If the set of...
The method of antithetic variates is a technique for reducing the variance of simulation estimators. Antithetic variates are negatively correlated random variables that share a common mean and common...
What approaches to recruitment can an employer adopt in order to create and project a positive public image?
Suppose Hondas total cost of producing 4 cars is $225,000 and its total cost of producing 5 cars is $250,000. What is the average total cost of producing 5 cars? What is the marginal cost of the...
Super Markets Inc. is considering expanding into the Scottsdale, Arizona, area. You, as director of planning, must present an analysis of the proposed expansion to the operating committee of the...
Water to run a Pelton wheel is supplied by a penstock of length $\ell$ and diameter $D$ with a friction factor $f$. If the only losses associated with the flow in the penstock are due to pipe...
Reagan Corporation is a wholesale distributor of truck replacement parts. Initial amounts taken from Reagan's records are as follows: Inventory at December 31 (based on a physical count of goods in...
The information for Bland Media Company at the end of the fiscal year, June 30, 20X8 are listed in this spreadsheet . Additional information: Capital were $145000 at May 1, 20X7, additional capital...
A food company produces tomato sauce at five different plants. The tomato sauce is then shipped to one of three warehouses, where it is stored until it is shipped to one of the companys four...
These prove that isomorphism is an equivalence relation. (a) Show that the identity map id: V V is an isomorphism. Thus, any vector space is isomorphic to itself. (b) Show that if f: V W is an...
Show that each type of map from Example 1.8 is an automorphism. (a) Dilation ds by a nonzero scalar s. (b) Rotation t through an angle . (c) Reflection f over a line through the origin.
Study each of the following cases carefully. Briefly state the principle of law and your decision. The law in a particular state provided that the commissioner of insurance had the authority to...
The results of the fatigue testing for a hip joint that your company has developed are depicted below. Walking normally places a load on the hip that is equal to about 2.5 times body weight. Jogging...
Yellow light ( \ lambda = 5 8 0 nm ) is incident upon a diffraction grating which has 7 0 0 lines per millimeter. The first bright spot is found to be 6 8 cm away from the center. If you, instead,...
2.88 A gate having the shape shown in Fig. P2.88 is located in the vertical side of an open tank containing water. The gate is mounted on a horizontal shaft. (a) When the water level is at the top of...
You have an algorithm called "k-Means-Medians-Modes". It takes into consideration the mean, median and mode simultaneously of each cluster. (a) Do you think this algorithm would perform well ?...
Find the domain of the given rational function. (x-4) 2x - 9x-18 f(x)= = The domain of f is
What is meant by cost accounting records, and what is their importance in the conduct of an audit?
The maximum pressure that can be developed for a certain fluid power cylinder is 15.0 MPa. Compute the required diameter for the piston if the cylinder must exert a force of 30 kN.
In Exercises 1 and 2, choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. Give separate answers for each part. 1. x1 + hx2 = 2 4x1 C 8x2 = k 2. x1...
In Exercises 1 and 2, mark each statement True or False. Justify each answer. 1. a. In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different...
Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution.
Giving a test to a group of students, the grades and gender are summarized below A B C Total Male Female 10 3 15 28 8 20 19 47 Total 18 23 34 75 If one student is chosen at random, Find the...
K A universal set U consists of 16 elements. If sets A, B, and C are proper subsets of U and n(U) 16, n(An B) = n(An C) = n(BNC) = 6, n(AnBn C) = 2, and n(A UBU C) = 14, determine each of the...
Without solving, say whether the equation has two solutions, one solution, or no solution. The equation has because (x+4) = 19

Suppose that f: V W preserves structure. Show that f is one-to-one if and only if

Question:

Step by Step Answer:

One direction is easy by definition if f is onetoone ...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions