Solve a system of linear equations By reducing

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 1 1 0

Replace row 2 with row 2 – row 1

Replace row 2 with row 2 – row 1 -1

Replace row 2 with row 2 – row 1 -1 0 0 1 1

Replace row 3 with row 3 – 3 row 1

Replace row 3 with row 3 – 3 row 1 -3

Replace row 3 with row 3 – 3 row 1 -3 0 0 1 1

Replace row 3 with row 3 – row 2

Replace row 3 with row 3 – row 2 -1

Replace row 3 with row 3 – row 2 -1 0 0

Replace row 1 with row 1 – row 2

Replace row 1 with row 1 – row 2 -1

Replace row 1 with row 1 – row 2 0 -1 -1

The matrix is in REDUCED ECHELON FORM

The matrix is in REDUCED ECHELON FORM 1 1 Every FNZE is a 1 First Non. Zero Entry in a row of a matrix

The matrix is in REDUCED ECHELON FORM 1 1 1 Every FNZE is a Every FNZE is to the right of the FNZE above it.

The matrix is in REDUCED ECHELON FORM 1 0 0 1 0 Every FNZE is a Every FNZE is to the right of the FNZE above it. In a column containing a FNZE, every other element is a 0

Interpret :

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