Question: Let T: R n R n be a linear transformation. a. What is the dimension of the range of T if T is a

Let T: R^{n →}Rⁿ be a linear transformation.

a. What is the dimension of the range of T if T is a one-to- one mapping? Explain.

b. What is the dimension of the kernel of T if T maps Rⁿ onto R^m? Explain.

Step by Step Solution

★★★★★

3.35 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER a If T is a onetoone mapping then every vector in the domain of T maps to a unique vector in the range of T In other words if Tx Ty then x y fo... 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

Students Have Also Explored These Related Linear Algebra And Its Applications Questions!

Let L: Rn Rm be a linear transformation defined by L(x) = Ax, for x in R". Prove that L is onto if and only if rank A = m.

Let T be a linear transformation from R2 to R2 (or from R3 to R3). Prove that T maps a straight line to a straight line or a point.

Let T: R2 P2 be a linear transformation for which Find =1-2x and T x+2x2 0 and T

Problem 13. (1 point) Problem 19. (1 paint) Are the following statements true or false? Let A = 4 5 and w = 7 1. If A is a 7 x 5 matrix, and I(x) - Ar is a linear transfor- Is win Cal(A)? Type "yes"...

QUESTION 1 V Select the mappings that are linear transformations Choose all that apply . 5 points Select the mappings that are linear transformations T : R - R such that T(x) = 21 T : R' -+ R such...

8.1 WRITE on paper for upvote. Section: 25, 32, 33 please 8.1 General Linear Transformations 20. Consider the basis S = {V1, V2} for R', where v, = (-2, 1) and 9. T : Rx - R., where V2 = (1, 3), and...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

Math 21 Winter 2017 Professor Bruce Cooperstein Final Review/Practice Examination You will need to know the definitions of the following in order to do the questions on the examination. You will not...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Inventory information for Part 311 of Monique Aaron Corp. discloses the following information for the month of June. June 1 Balance 300 units .... @ $10 11 Purchased 800 units .... @ $12 20 Purchased...

The controller of Furgee Industries has collected the following monthly expense data for use in analyzing the cost behavior of maintenance costs. Instructions (a) Determine the fixed- and...

Pregunta 8 ( 1 punto ) Qu papel juega el p ncreas en la digesti n de las prote nas ? Produce proteasa Libera tripsina Absorbe pepsina Ay B

12.5 Develop a preparation outline and speaking notes for a speech. A final step before beginning to rehearse your speech is to prepare a detailed preparation outline and speaking notes. Your...

It has been stated that the normal distribution is really a family of distributions. Explain.

In the normal distribution, the probability that x will exceed ( + 2) is the same as the probability that x will be less than ( - 2). What characteristic of the normal distribution does this reflect?

Sketch two different normal distributions along a single x axis so that both of the following conditions are satisfied: (a) a = b and b a > b .

For the year ended June 30, 2017, Sunland Clothing Company has total assets of $90,000,000, ROA of 9.00 percent, ROE of 12.00 percent, and a net profit margin of 8.00 percent. What are the company's...

On Dec 1st 2000, A Pharmaceutical company, Pharma plc, acquires 80% shares of a start-up business, Vac for 1,200, 000 . The payment is made by cash on Dec 1st. Vac is performing highly innovative...

19 Perpetual Inventory Using FIFO Beginning inventory, purchases, and sales for Item Zeta9 are as follows: Assuming a perpetual inventory system and using the first-in, first-out (FIFO) method,...