Understanding 2x2 Matrices and Transformations

What is the significance of the 1 0 vector in the coordinate plane?

• It represents a diagonal movement.

• It represents a unit movement in the y direction.

• It represents a unit movement in the x direction.

• It represents no movement in any direction.

How can any point on the coordinate plane be expressed?

• As a product of two vectors.

• As a difference between two vectors.

• As a weighted sum of the 1 0 and 0 1 vectors.

• As a sum of two identical vectors.

What does the identity transformation do to a point on the coordinate plane?

• It leaves the point unchanged.

• It reflects the point across the y-axis.

• It moves the point to the origin.

• It rotates the point 90 degrees.

What transformation is represented by a 2x2 matrix with columns 1 0 and 0 1?

• Reflection

• Rotation

• Scaling

• Identity

In a non-identity transformation, what happens to the 1 0 vector?

• It remains unchanged.

• It becomes a 0 1 vector.

• It disappears.

• It transforms into a new vector, such as 2 1.

How does a 2x2 matrix affect a triangle on the coordinate plane?

• It can only rotate the triangle.

• It can make the triangle disappear.

• It can map the triangle to another triangle.

• It can turn the triangle into a circle.

What is the result of applying a non-identity transformation to a point?

• The point is mapped to a new location.

• The point is deleted from the plane.

• The point remains unchanged.

• The point is duplicated.

What is a key property of linear transformations?

• They can map lines to curves.

• They can change the dimensionality of a space.

• They always map the origin to itself.

• They can only be represented by 3x3 matrices.

What happens to a point at the origin during a linear transformation?

• It scales by a factor of two.

• It reflects across the x-axis.

• It remains at the origin.

• It moves to a new location.

Can a 2x2 matrix perform a rotation transformation?

• Yes, as long as the origin remains fixed.

• No, rotations are not possible with matrices.

• No, rotations require a 3x3 matrix.

• Yes, but only if the origin is moved.