# Elementary Row Operations

## Key Questions

• The transpose of a matrix is found by creating new matrix where the rows and columns are swapped out. If i denotes row and j denotes column, we have ${a}_{i j}$ becomes ${a}_{j i}$.

Suppose you have a matrix A. The transpose is denoted ${A}^{T}$. Let us take a 2 x 2 matrix for simplicity.

${a}_{11}$ is row 1, column 1. The transposed entry would stay the in the same place.

${a}_{12}$ is row 1, column 2. The transposed entry would be placed in Row 2, Column 1${a}_{21}$.

${a}_{21}$ is row 2, column 1. The transposed entry would be placed in Row 1, Column 2${a}_{12}$.

${a}_{22}$ is row 2, column 2. The transposed entry would stay in the same place.

• There are three elementary row operatins of matrices:

• Exchange two rows position;

• Substitute a row for the sum of it and another row;

• Multiply a row for a scalar;

Hop it helps.