Nonsquare matrices as transformations between dimensions: Essence of Linear Algebra - Part 8 of 15

What is a key characteristic of a linear transformation?

• Vectors rotate around a fixed point.

• The origin shifts to a new position.

• Vectors change their magnitude randomly.

• Grid lines remain parallel and evenly spaced.

How is a transformation from 2D to 3D represented?

• With a 2x3 matrix.

• With a 3x3 matrix.

• With a 2x2 matrix.

• With a 3x2 matrix.

What does a 3x2 matrix indicate in terms of dimensions?

• Mapping from 3D to 3D.

• Mapping from 2D to 2D.

• Mapping from 2D to 3D.

• Mapping from 3D to 2D.

What does a transformation from 3D to 2D involve?

• Mapping three basis vectors to three coordinates.

• Mapping two basis vectors to two coordinates.

• Mapping two basis vectors to three coordinates.

• Mapping three basis vectors to two coordinates.

What is the visual understanding of linearity in a 2D to 1D transformation?

• The origin shifts to a new position.

• Vectors rotate around the origin.

• Grid lines become curved.

• Evenly spaced dots remain evenly spaced on the number line.