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Chapter 1 Section 2
Example 1: R1+R2 R2 2R1+R3 R3 R5-R1 R5
Example 1: R1+R2 R2 2R1+R3 R3 R5-R1 R5 A system is said to be in strict triangular form if, in the kth equation, the coefficients of the first k-1 variables are all zero and the coefficients of the x k is nonzero (k=1,…,n)
Example 1: R3-2R2 R3 R4-R2 R4 R5-R2 R5
Example 1: R4-R3 R4 R3-R5 R5
Example 2: R1+R2 R2 2R1+R3 R3 R5-R1 R5
Example 2: R3-2R2 R3 R4-R2 R4 R4-R3 R4 R5-R4 R5
Which matrices are in Row Echelon form? No Violates Rule 1 Yes No Violates Rule 3 No Violates Rule 2 Yes
Example 4: System A R1-R2 R2 ½R2 R2 R1+R3 R3 3R2-R3 R3 -½ R3 R3
Example 4: System B 2R1-R2 R2 4R1-R3 R3 2R1-R4 R4 R2-R3 R3 R3 R4
Example 4: System B R2-R3 R3 ⅕ R2 R2 ½R3 R3
Example 4: System C 2R1-R2 R2 4R1-R3 R3 R2-R3 R3 R3 R4 3R1-R3 R3
Example 4: System C R2-R3 R3 ⅕ R2 R1
Example 5: System A 2R1-R2 R2 -R2 R2
Example 5: System B R2-R1 R2 R3-R1 R3 R3-R2 R3 R2-R3 R2 R1-R3 R1 R1-R2 R1
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Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 1.
Using Matrices A matrix is a rectangular array that can help us to streamline the solving of a system of equations The order of this matrix is 2 × 3 If.
8.1 Matrices and Systems of Equations. Let’s do another one: we’ll keep this one Now we’ll use the 2 equations we have with y and z to eliminate the y’s.
Recall that when you wanted to solve a system of equations, you used to use two different methods. Substitution Method Addition Method.
Differential Equations Linear Equations with Variable Coefficients.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter 1 Matrices and Systems of Equations. 1Systems of Linear Equations Where the a ij ’s and b i ’s are all real numbers, x i ’s are variables. We.
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Chapter 3 Determinants Linear Algebra. Ch03_2 3.1 Introduction to Determinants Definition The determinant of a 2 2 matrix A is denoted |A| and is given.
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7.3 & 7.4 – MATRICES AND SYSTEMS OF EQUATIONS. I N THIS SECTION, YOU WILL LEARN TO Write a matrix and identify its order Perform elementary row operations.
How To Find The Reduced Row Echelon Form. Reduced Row Echelon Form A matrix is said to be in reduced row echelon form provided it satisfies the following.
Sec 3.1 Introduction to Linear System Sec 3.2 Matrices and Gaussian Elemination The graph is a line in xy-plane The graph is a line in xyz-plane.
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CHAPTER 8.1 Matrices and Systems of Equations. Matrix- a streamlined technique for solving systems of linear equations that involves the use of a rectangular.
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