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Q1/ Give the mathematical interpretation for the following items ( enhance your answer with a mathematical proof for each item below) a- For the two nxn matrices A and B, (AB)'= B'A" V b- For a symmetric nxn matrix A. then: P=P", p=-p , none of them. c- If D" =x'A" X, then A" = X'D"X , wherekis a positive integer. d- The solution homogeneous set of equations when D = |A|#0, has consistent, inconsistent or infinity solutions. Why ? e- The benefit of Gamma function . Find r(n-1). f-The elementary matrix, the modal matrix , echelon matrix.

Q1/ Give the mathematical interpretation for the following items ( enhance your answer with a mathematical proof for each item below) a- For the two nxn matrices A and B, (AB)'= B'A" V b- For a symmetric nxn matrix A. then: P=P", p=-p , none of them. c- If D" =x'A" X, then A" = X'D"X , wherekis a positive integer. d- The solution homogeneous set of equations when D = |A|#0, has consistent, inconsistent or infinity solutions. Why ? e- The benefit of Gamma function . Find r(n-1). f-The elementary matrix, the modal matrix , echelon matrix.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Q1/ Give the mathematical interpretation for the following items ( enhance your answer with a mathematical proof for each item below) a- For the two nxn matrices A and B, (AB)' = B'A" V b- For a symmetric nxn matrix A. then: P=P", p=-p, none of them. c- If D" =X'A" X , then A" = X'D"X , wherekis a positive integer. d- The solution homogeneous set of equations when D = |A|#0, has consistent, inconsistent or infinity solutions. Why ? e- The benefit of Gamma function. Find r(n-1). f-The elementary matrix, the modal matrix , echelon matrix.
Transcribed Image Text:Q1/ Give the mathematical interpretation for the following items ( enhance your answer with a mathematical proof for each item below) a- For the two nxn matrices A and B, (AB)' = B'A" V b- For a symmetric nxn matrix A. then: P=P", p=-p, none of them. c- If D" =X'A" X , then A" = X'D"X , wherekis a positive integer. d- The solution homogeneous set of equations when D = |A|#0, has consistent, inconsistent or infinity solutions. Why ? e- The benefit of Gamma function. Find r(n-1). f-The elementary matrix, the modal matrix , echelon matrix.
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