Let M2(R) be the set of 2 x 2 matrices with real cntrics. That is: M,(R) = {[: ] maadeR}. "(::)- Consider the function T: M,(R) R defined by T = (a + d,a – c). c d Fal 7 ()- 1. Find T 3 4 2. Show that T is not injective. 3. Show that F is surjective.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

need help 

Let M2(R) be the set of 2 x 2 matrices with real entries. That is:
a b
M2(R) = {" a, b, c, d e R
Consider the function T: M, (R)R defined by T
(:2)- (a+d,a=e).
->
(:)-
1 2
3 4
1. Find T
2. Show thatT is not injective.
3. Show that T is surjective.
Transcribed Image Text:Let M2(R) be the set of 2 x 2 matrices with real entries. That is: a b M2(R) = {" a, b, c, d e R Consider the function T: M, (R)R defined by T (:2)- (a+d,a=e). -> (:)- 1 2 3 4 1. Find T 2. Show thatT is not injective. 3. Show that T is surjective.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,