Transformation Matrices and Their Effects

The video tutorial explains how to match transformation matrices with their effects on vectors in R2. It covers three matrices: P, S, and R. Matrix P reflects vectors across the line y = -x, Matrix S projects vectors onto the line y = x, and Matrix R rotates vectors 90 degrees clockwise. Each matrix's columns represent transformations of standard basis vectors, and the video demonstrates how to graph these transformations and interpret their effects.

What does the first column of a transformation matrix in R2 represent?

• The transformation of vector e1

• The transformation of vector e2

• The transformation of vector e3

• The transformation of vector e4

Which line do vectors reflect across when transformed by matrix P?

• y = x

• y = -x

• y = 0

• x = 0

What is the effect of matrix P on the vector e1?

• It scales e1 by a factor of 2

• It transforms e1 to (0, -1)

• It reflects e1 across the line y = x

• It rotates e1 by 90 degrees

Which matrix reflects vectors across the line y = -x?

• Matrix S

• Matrix P

• Matrix Q

• Matrix R

What is the transformation effect of matrix S on vectors?

• Scales vectors by a factor of 3

• Reflects vectors across y = -x

• Rotates vectors 180 degrees

• Projects vectors onto y = x

How does matrix S transform the vector e2?

• It transforms e2 to (1, 0)

• It transforms e2 to (-1, 0)

• It transforms e2 to (0, 1)

• It transforms e2 to (1/2, 1/2)

Which matrix projects vectors onto the line y = x?

• Matrix P

• Matrix Q

• Matrix S

• Matrix R

What is the effect of matrix R on the vector e1?

• It rotates e1 by 90 degrees clockwise

• It reflects e1 across the line y = x

• It transforms e1 to (1, 0)

• It scales e1 by a factor of 2

Which direction does matrix R rotate vectors?

• 90 degrees clockwise

• 180 degrees

• No rotation

• 90 degrees counterclockwise

What is the transformation of vector e2 by matrix R?

• It transforms e2 to (-1, 0)

• It transforms e2 to (1, 0)

• It transforms e2 to (0, -1)

• It transforms e2 to (0, 1)