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EE:211 Computational Techniques in Electrical Engineering Lecture#6 Dr. Mubashir Alam King Saud University
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Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

Dec 27, 2015

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Page 1: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

EE:211Computational Techniques in

Electrical Engineering Lecture#6

Dr. Mubashir AlamKing Saud University

Page 2: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

OutlineSystems of Linear Equations (6.1)Matrix Arithmetic (6.2)

Arithmetic Operations (6.2.1)Elementary Row Operations (6.2.2)The Matrix Inverse (6.2.3)Matrix Algebra Rules (6.2.4)Solvability Theory of Linear Systems (6.2.5)

Page 3: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 4: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 5: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

Matrix: (n x n)Known

Vector: (n x 1)Known

Vector: (n x 1)Unknown

Page 6: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

Square Matrix m=n

Elements of matrix

Page 7: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 8: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 9: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 10: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 11: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 12: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 13: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 14: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

If and only if det(A)≠ 0

Page 15: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

Special MatricesDiagonal MatrixUpper Triangular MatrixLower Triangular MatrixSymmetric Matrix

Page 16: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

R1-R2R2-R3

Page 17: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

R1-R2

R3-2R1

Page 18: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

Matrix Algebra RulesCovered on Textbook: Page:256

Page 19: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 20: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.
Page 21: Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.