What would you like to understand?

We create a $2 \times 2$ matrix where the first column records the coordinates of where $\hat{i}$ lands, and the second column records the coordinates of where $\hat{j}$ lands. This matrix fully represents the linear transformation.

Conditions: Working in 2D space.; Knowing the images of $\hat{i}$ and $\hat{j}$.

We create a $2 \times 2$ matrix where the first column records the coordinates of where $\hat{i}$ lands, and the second column records the coordinates of where $\hat{j}$ lands. This matrix fully represents the linear transformation.

Conditions: Working in 2D space.; Knowing the images of $\hat{i}$ and $\hat{j}$.