18.02SC | Fall 2010 | Undergraduate

# Multivariable Calculus

1. Vectors and Matrices

## Part B: Matrices and Systems of Equations

« Previous | Next »

The basic point of this part is to formulate systems of linear equations in terms of matrices. We can then view them as analogous to an equation like 7_x_ = 5.

In order to use them in systems of equations we will need to learn the algebra of matrices; in particular, how to multiply them and how to find their inverses.

Geometrically, a linear equation in x, y and z is the equation of a plane. Solving a system of linear equations is equivalent to finding the intersection of the corresponding planes.

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Watch a recitation video
• Do problems and use solutions to check your work

### Lecture Video

#### Video Excerpts

Clip: Matrix Multiplication

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Matrices (PDF)

### Problems and Solutions

Problems: Matrix Multiplication (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Do the problems
• Use the solutions to check your work

### Problem Set

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Do problems and use solutions to check your work

### Lecture Video

#### Video Excerpts

Clip: Meaning of Matrix Multiplication

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

### Reading and Examples

Meaning of Matrix Multiplication (PDF)

### Problems and Solutions

Problems: Meaning of Matrix Multiplication (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Watch a recitation video
• Do problems and use solutions to check your work

### Lecture Video

#### Video Excerpts

Clip: Matrix Inverses

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

### Reading and Examples

Matrix Inverses (PDF)

### Problems and Solutions

Problems: Matrix Inverses (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Watch a recitation video
• Do problems and use solutions to check your work
• Watch another recitation video
• Read more course notes and examples
• Do another set of problems and use solutions to check your work

### Lecture Video

#### Video Excerpts

Clip: Equations of Planes

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

### Reading and Examples

Equations of Planes (PDF)

### Problems and Solutions

Problems: Equations of Planes (PDF)

Solutions (PDF)

### Reading and Examples

Distances to Planes and Lines (PDF)

### Problems and Solutions

Problems: Distances to Planes and Lines (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes
• Do problems and use solutions to check your work

### Lecture Video

#### Video Excerpts

Clip: Linear Systems and Planes

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Geometry of Linear Systems (PDF)

### Problems and Solutions

Problems: Geometry of Linear Systems (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes
• Review an example
• Watch a recitation video
• Do problems and use solutions to check your work

### Lecture Video

#### Video Excerpts

Clip: Solutions to Square Systems

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Homogeneous and Inhomogeneous Systems (PDF)

### Examples

Solutions to Linear Systems (PDF)

### Problems and Solutions

Problems: Solutions to Linear Systems (PDF)

Solutions (PDF)

« Previous | Next »

## Course Info

Fall 2010
##### Learning Resource Types
Simulations
Exams with Solutions
Problem Sets with Solutions
Lecture Videos
Lecture Notes