Matrices as transformations
A matrix moves the points of the plane: apply it to a point, build it from the images of i and j and find the points it leaves in place.
- إيران: الصف ١٢
- أفغانستان: الصف ١١
- ألمانيا: الصف ١٠
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
A 2 × 2 matrix times the column of a point (x, y) gives the image of that point. The matrix with rows 1 0 and 0 −1 sends (x, y) to (x, −y): a reflection in the x-axis. This is how the Afghan book begins the chapter.
The columns of the matrix are the images of the points (1, 0) and (0, 1). Knowing where these two go, you know the whole matrix.
A vector that the matrix sends to itself is invariant: Av = v. For a reflection in a line, the points on the line are invariant.
Ask your child to picture the transformation before multiplying. Is it a turn, a reflection or a stretch?