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Solve a system of linear equations. By reducing a matrix. Pamela Leutwyler. Describe the solutions to:. Describe the solutions to:. The coefficient matrix:. Replace row 1 with row 1 – row 2. Replace row 1 with row 1 – row 2. 1. 1. 0. 1. -1.
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Solve a system of linear equations By reducing a matrix Pamela Leutwyler
Describe the solutions to: The coefficient matrix:
Replace row 1 with row 1 – row 2 1 1 0 1 -1
Replace row 2 with row 2 – row 1 -1 0 1 1 0
Replace row 3 with row 3 – 3 row 1 -3 0 1 1 0
Replace row 1 with row 1 – row 2 0 -1 -1
The matrix is in REDUCED ECHELON FORM 1 1 Every FNZE is a 1 First NonZero Entry in a row of a matrix
The matrix is in REDUCED ECHELON FORM 1 1 Every FNZE is a 1 Every FNZE is to the right of the FNZE above it.
The matrix is in REDUCED ECHELON FORM 0 1 0 1 0 0 Every FNZE is a 1 Every FNZE is to the right of the FNZE above it. In a column containing a FNZE, every other element is a 0
Interpret : w= -x +z
Interpret : w= -x +z y= -z
Interpret : w= -x +z y= -z
Interpret : w= -x +z x= x y= -z z= z x and z are the independent variables
Interpret : w= -x +z x= x y= -z z= z
Interpret : Every solution is a linear combination of these vectors