Matrices

• What is the result of adding a and b?

  a (+) and b (+)
• What does the commutative property state for addition?

  AB = BA
• Is the commutative property applicable to multiplication?

  No, it is not for multiplication
• What do columns represent in a matrix?

  Rows in second
• What does the associative property state?

  ABC = A(BC) = (AB)C
• What does the distributive property state?

  A(B + C) = AB + AC
• How is the determinant of a 2x2 matrix calculated?

  d = ad - bc
• What does transposing a matrix involve?

  Rows swap with columns
• What does it mean if the determinant is 0?

  It is singular and has no inverse
• How can you show two matrices are inverses?

  Multiply and will equal identity matrix
• What is the angle of a 90-degree rotation?

  90 degrees
• What is the angle of a 180-degree rotation?

  180 degrees
• What direction does a 90-degree clockwise rotation go?

  Clockwise
• What direction does a 90-degree anticlockwise rotation go?

  Anticlockwise
• What trigonometric functions are associated with rotation?

  Sine and cosine
• What are the properties of matrix operations?

  • Commutative: AB = BA (not for multiplication)
  • Associative: ABC = A(BC) = (AB)C
  • Distributive: A(B + C) = AB + AC
• What are the implications of a determinant being zero?

  • The matrix is singular
  • The matrix has no inverse
• identity matric is

  1 0

  0 1
• to transpose the rows swape with columns
• detmn = detm * detn
• 90 degrees anti clockwise

  0 -1

  1 0
• 180 degrees is

  -1 0

  0 -1
• 90 degree clockwise is

  0 1

  -1 0
• anticlockwise rotation

  cos -sin

  sin cos
• reflection in the x axis

  1 0

  0 -1
• reflection in the y axis

  -1 0

  0 1
• reflection of y=x

  0 1

  1 0
• reflection for y=-x

  0 -1

  -1 0
• reflection in general line y=xtan

  cos2 sin2

  sin2 -cos2
• reflection of y=xtan

  ++

  +-
• rotation of y=xtan

  +-

  ++
• What is a key property of matrix multiplication?

  It is not commutative
• What is the identity matrix?

  A matrix that does not change other matrices
• What happens when you transpose a matrix?

  Columns swap with rows
• How is the determinant of a 2x2 matrix calculated?

  det = ad - be
• What is the purpose of the inverse of a matrix?

  To find a matrix that, when multiplied, gives the identity matrix
• What does det() represent?

  The determinant of a matrix
• What are the types of 2D transformations in matrices?

  • Rotation (90° anticlockwise)
  • Rotation (180°)
  • Rotation (90° clockwise)
  • Reflection across x-axis
  • Reflection across y-axis
  • Reflection across y=x
• What is the result of a 90° anticlockwise rotation of a point?

  Coordinates change according to rotation rules
• What is the result of a 180° rotation of a point?

  Coordinates are inverted