G. Conjugate of a Matrix 3 - i -3i 6+ 21], k = -3, c = -1+ 2i 5- 4il 4+i Let A = B = 15+2i 3i and the following are the properties of the conjugate of a matrix. Verify the following equivalence. 1. Å = A. 2. Á+B = Ã + B. = B. 3. AB =

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
icon
Related questions
Question
G. Conjugate of a Matrix
Let A = [4 +i 3- i
Is+ 2i 1.
-3i 6+ 2i]
B =
7
5- 4il
k = -3, c= -1+ 2i
and the following are the properties of the conjugate of a matrix. Verify the following
equivalence.
1. A A.
2. A+B = Ã+ B.
à B.
3. АВ 3D
real number k, kà = kA.
CÃ = CA.
4. For
any
5. For any complex number c,
%3D
6. (Ã)" = A
7. If A is nonsingular, then (A)= A-1
Transcribed Image Text:G. Conjugate of a Matrix Let A = [4 +i 3- i Is+ 2i 1. -3i 6+ 2i] B = 7 5- 4il k = -3, c= -1+ 2i and the following are the properties of the conjugate of a matrix. Verify the following equivalence. 1. A A. 2. A+B = Ã+ B. à B. 3. АВ 3D real number k, kà = kA. Cà = CA. 4. For any 5. For any complex number c, %3D 6. (Ã)" = A 7. If A is nonsingular, then (A)= A-1
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax