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Chapter 1 MAT188H1F Lec03 Burbulla Chapter 1 Lecture Notes Fall 2007 Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 Chapter 1 Homogeneous Systems Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla
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Chapter 1 Homogeneous Systems What Is A Homogeneous System of Equations? If all the constants to the right of the equal signs in a system of linear equations are zero, then the system is called a homogeneous system of linear equations. That is, the augmented matrix of a homogeneous system looks like ( A | O ) where A = [ a ij ] is the m × n matrix of coefficients, and B = O is the all-zero m × 1 column vector of constants. Note: a homogeneous system of equations is consistent; there is always at least one solution, namely x 1 = 0 , x 2 = 0 , x 3 = 0 , . . . , x n = 0 . This is called the trivial solution. Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 Homogeneous Systems Example 1 Consider the system of equations x 1 - 2 x 2 + x 3 + x 4 = 0 - x 1 + 2 x 2 + x 4 = 0 2 x 1 - 4 x 2 + x 3 = 0 It’s augmented matrix is 1 - 2 1 1 0 - 1 2 0 1 0 2 - 4 1 0 0 Row reduction gives 1 - 2 1 1 0 - 1 2 0 1 0 2 - 4 1 0 - 0 1 - 2 1 1 0 0 0 1 2 0 0 0 - 1 - 2 0 Chapter 1 Lecture Notes
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