Destiny M. answered • 05/26/19

Math Major; English and Math Tutor

2x_{1} + x_{2} - 2x_{3}

4x_{1 }+ 3x_{2}

3x_{1} + 2x_{2} - x_{3}

Now we we will use Gaussian Elimination:

[2 1 -2]

[4 3 0] (R_{2} = -2R_{1 }+ R_{2})

[3 2 -1] (R_{3 }= -3R_{1 }+ 2R_{1})

[2 1 -2]

[0 1 4]

[0 1 4] (R_{3} = R_{2} - R_{3})

[2 1 -2]

[0 1 4]

[0 0 0] This is now in row echelon form. There is a pivot in the first row (2) and there is a pivot in the second row (1). There is no pivot in the third row, however, because the bottom row of the matrix only contains zero's and thus the matrix is not in upper triangular form (google upper triangular matrix). Since there is not a pivot in every row, T is not linearly independent.