Suppose that T: U V is a surjective linear transformation and dim (U) = dim (V).

Question:

Suppose that T: U → V is a surjective linear transformation and dim (U) = dim (V). Prove that T is injective.

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 02:42 AM

See More Questions

Prove: There can be a surjective linear transformation from V to W only if dim(v) dim (W).
Suppose that T: U V and S: V W are linear transformations. Prove the following relationship between ranges. R(S T) R(S)
Suppose that T: U V and S: V W are linear transformations, and that B, C and D are bases for U, V, and W. Using only Definition MR define matrix representations for T and S. Using these two...
A newly issued 20-year maturity, zero-coupon bond is issued with a yield to maturity of 8% and face value $1,000. Find the imputed interest income in the first, second, and last year of the bonds...
Discuss whether each statement is a purely positive statement, or also contains normative elements and/or value judgments: a. An increase in the personal income tax will slow the growth rate of the...
1. Why does Kass suggest that the concern for biotechnological enhancement may be a touch self-indulgent? 2. How does Kass call into question the distinction between therapy and enhancement? 3. What...
True or False: A rotor that has been installed in the field, experiences a rise in vibration levels and the ends are in phase. Eventually, the vibration levels call for the machine to be taken off...
The Taylor Corporation has a machining facility specializing in jobs for the aircraft- components market. Taylors previous simple job- costing system had two direct- cost categories (direct materials...
Discuss/debate with your classmates about the early history of the criminal theory and its application to crime control i.e., Positivist School vs. Classical School, plus gender, class, and race as...
PepsiCo produces snack foods such as Fritos and Lay's potato chips, as well as beverages such as Pepsi and Mug Root Beer. The company had the following condensed trial balance as of September 3,...
The linear transformation R: M12 M21 is invertible. Determine a formula for the inverse linear transformation R-1: M21 M12. a + 3b
Suppose that U and V are isomorphic vector spaces. Prove that there are infinitely many isomorphisms between U and V.
In Problems 514, solve for x by writing the equation inexponential form. log 7 (3x + 1) = 2
In mathematics, Pythagoras' theorem is a relation in geometry among the three sides of a right triangle. The theorem states that the square of the hypotenuse (the side opposite the right angle) is...
Consider a memory location A has (01011101)b, What will be the binary value stored in memory Location A in after executing the following piece of code. Rotate Left A,4 LSHR A, 2 Answer: Activate...
An analysis has been undertaken by the industrial engineering staff in consultation with the activity managers.The activity listed below can be crashed. Reduce the project duration as much as cost...
3) a) Create a "house" class that initializes house objects in the following way: hl=House(Location,Age,R_Number,Price) Location: Location of the house Age: Age of the house R_Number:Number of the...
Consider the following code written below: public interface A{ public String STR = "BCS2143"; public boolean number (int num); public String setUpperCase (String str); } public class B{} public class...
Renee and Sanjeev Patel, who are married, reported taxable income of $1,008,000 for 2021. They incurred positive AMT adjustments of $75,000 and tax preference items of $67,500. The couple itemizes...
Which of the following is FALSE regarding the purchasing power parity (PPP). a. The PPP is a manifestation of the law of one price b. The PPP says that a country with a higher expected inflation can...
Find the dimension of and a basis for the subspace spanned by the following sets of vectors. (a) (b) (c) (d) (e) 121 3 1233 2210 1001 1010 90000 13121 034011 21221 10320
Show that the set of all vectors of the v = (a - 3b. a +2c + 4d. b + 3c - d, c - d)T . where a, b.c.d are real numbers, forms a subspace of R4, and find its dimension.
Find a basis of the solution space of the following homogeneous linear systems. (a) x1 - 2x3 - 0, x2 +x4 = 0. (b) 2x1 + x2 - 3x3 + x4 = 0, 2x1 - x2 - x3 - x4 = 0. (c) x1 -x2 - 2x3 + 4x4 = 0, 2x1 +x2...
Consider a hedonic pricing model for educational attainment. Would isoprofit curves for the firm be upward or downward sloping? Explain. Question 2 (Mandatory) (3 points) Listen For workers, would...
6. Determine the sum of the measures of the interior angles of this polygon.
Consider the perfectly competitive Corn industry. It is initially in long run equilibrium at quantity Q0 and price P0. a) Draw a supply and demand diagram for the Corn market showing this...

Suppose that T: U V is a surjective linear transformation and dim (U) = dim (V).

Question:

Step by Step Answer:

If T is surjective then Theorem RSLT says RT V so r T dim by Definit...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions