Linear Algebra

Kathryn Peake, May 29, 2018

Table of Contents

  1. Introduction
    1. Linear mappings
    2. Linear functions in 2-D
  2. Equations of lines
    1. Vector Equation of a Line (2D)
    2. Vector equation of a line (3D)
    3. Vector Equation of a Line (3D) v2
    4. Vector Equations of 2 Lines (3D)
    5. Vector Equations of 2 Lines (3D) v2
  3. Matrices
    1. Matrix addition
  4. Simultaneous equations
    1. Simultaneous equations as vector sums
    2. Intersection of 3 planes
    3. Intersection of Three Planes
    4. Simultaneous equations with 3 variables as sum of 3 vectors
  5. Matrices and transformations
    1. Linear Transformations 1
    2. Text book example
    3. Transformation of Unit Square
    4. MEI Rotation Matrix
    5. Invariance 1
    6. Invariance 2
    7. Invariance 3
    8. Invariance 4
    9. 3D Matrix Rotation
    10. Line reflection

1.

Introduction

  • 1. Linear mappings
  • 2. Linear functions in 2-D

1.1.

Linear mappings

Select each example in turn; move the slider; describe what you see.
– Kathryn Peake

1.2.

–

2.

Equations of lines

  • 1. Vector Equation of a Line (2D)
  • 2. Vector equation of a line (3D)
  • 3. Vector Equation of a Line (3D) v2
  • 4. Vector Equations of 2 Lines (3D)
  • 5. Vector Equations of 2 Lines (3D) v2

2.1.

Vector Equation of a Line (2D)

Follow the instructions given in class
– Kathryn Peake

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Matrices

  • 1. Matrix addition

3.1.

Matrix addition

– Kathryn Peake

4.

Simultaneous equations

  • 1. Simultaneous equations as vector sums
  • 2. Intersection of 3 planes
  • 3. Intersection of Three Planes
  • 4. Simultaneous equations with 3 variables as sum of 3 vectors

4.1.

Simultaneous equations as vector sums

– Kathryn Peake

4.2.

–

4.3.

–

4.4.

–

5.

Matrices and transformations

  • 1. Linear Transformations 1
  • 2. Text book example
  • 3. Transformation of Unit Square
  • 4. MEI Rotation Matrix
  • 5. Invariance 1
  • 6. Invariance 2
  • 7. Invariance 3
  • 8. Invariance 4
  • 9. 3D Matrix Rotation
  • 10. Line reflection

5.1.

Linear Transformations 1

Answer the questions below the diagram.
Find (a) the mapping and (b) the matrix that represent each of the following transformations:[br]1) Reflection in x-axis[br]2) Reflection in y-axis[br]3) Reflection in y = x[br]4) Reflection in y = -x[br]5) Rotation of 90[math]^\circ[/math] about O[br]6) Rotation of 180[math]^\circ[/math] about O[br]7) Rotation of 270[math]^\circ[/math] about O[br]8) Enlargement of SF k, centre of enlargement O[br]9) A sequence of two of the above transformations
– Kathryn Peake

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

5.7.

–

5.8.

–

5.9.

–

5.10.

–

Information