Posts Tagged ‘Row Operations’

Matrix Row Operations

Matrix Row Operations

 

a. Any two rows of the matrix may be interchanged.

 

b.  The numbers in any row may be multiplied by any nonzero real

 

c.  Any row may be transformed by adding to the numbers of the row the product of a real number and the corresponding numbers of another row.

Examples of these row operations follow.

 

Row operation 1:

\begin{bmatrix}  2 &3  &9 \\  4&8  &-3 \\  1& 0 & 7  \end{bmatrix} becomes \begin{bmatrix}  1 & 0 &7 \\  4& 8 & -3\\  2& 3 & 9  \end{bmatrix} . Interchange row 1 and row 3.

 

Row operation 2:

 

\begin{bmatrix}  2 &  3&9 \\  4 & 8 &-3 \\  1& 0 & 7  \end{bmatrix} becomes \begin{bmatrix}  6 &  9&27 \\  4& 8 &-3 \\  1&0  & 7  \end{bmatrix}. Multiply the number in row 1 by 3.

 

Row operation 3:

 

\begin{bmatrix}  2 & 3 &9 \\  4 & 8 & -3\\  1& 0 & 7  \end{bmatrix} becomes \begin{bmatrix}  0 & 3 &-5 \\  4& 8 & -3\\  1& 0 & 7  \end{bmatrix}. Multiply the number in row 3 by -2; add then to the corresponding numbers in row 1.

The third row operation corresponds to the way we eliminated a variable from a pair of equations in the previous sections.