VECTORS

• A vector quantity has both magnitude and direction. For example:
  • 
  • Vectors a and b represented by the line segments can be added using the parallelogram rule or the nose-to-tail method
• Multiplication by a scalar:
  • A scalar quantity has a magnitude but no direction.
  • The negative sign reverses the direction of the vector.
• Column vector:
  • 
  • The top number is the horizontal component and the bottom component is the vertical component.
• Parallel vectors:
  • Vectors are parallel if they have the same direction.
  • In general, the vector is parallel to
• Modulus of a vector:
  • In general, if

MATRICES

• Addition:
• Multiplication by scalar:
• Multiplication by vector:
  • You can only multiply if the number of columns on the left matrix is equal to the number of rows on the right matrix.
• Determinant:
  • Determinant = leading diagonal – secondary diagonal
  • 
• Inverse:
  • To work out the inverse of a matrix, alternate the leading diagonal’s elements, negate the secondary diagonal, and multiply by ¹/_determinant
  • 

TRANSFORMATION

• Reflection (M):
  • When describing a reflection, the position of the mirror line is essential.
• Rotation (R):
  • To describe a rotation, the center of rotation, the angle of rotation, and the direction of the rotation are required.
  • A clockwise rotation is negative and an anticlockwise rotation is positive.
• Translation (T):
  • When describing a translation, it is necessary to give the translation vector
• Enlargement (E):
  • To describe an enlargement, state the scale factor,k, and the center of enlargement.
  • 
  • If k > 0, both object and image lie on the same side of the center of enlargement.
  • If k < 0, object and image lie on opposite sides of the center of enlargement.

TRANSFORMATION BY MATRICES

• Reflection:
  • — Reflection in the x – axis
  • — Reflection in the y – axis
  • — Reflection in the line y = -x
• Enlargement:
  • — where k = scale factor and center of enlargement = (0, 0)
• Rotation:
  • — Rotation 90° anticlockwise, center (0, 0)
  • — Rotation 90° clockwise, center (0, 0)
  • — Rotation 180° clockwise/anticlockwise, center (0, 0)