1S11 (McLoughlin) Tutorial sheet 4
[Week 4, 2013]
Solutions
1. Find parametric equations for the line of intersection of the two planes
2x 4y + 3z = 1
2x + 2y + 2z = 3
Solution: We need a vector paral
1S11 (McLoughlin) Tutorial sheet 3
[Week 4 , 2013]
Name: Solutions
1. Find the equation of the plane in space passing through the point (1, 2, 3) perpendicular
(normal) to the vector 6i 5j + 4k.
Solut
Vectors
MA1S1
Tristan McLoughlin
[email protected]
Vectors
Some quantities (which we will call scalars) have purely numerical values
(like mass, volume, temperature) while others (which are called
1S11 (McLoughlin) Tutorial sheet 9
[Week 11, 2012]
1.
(a) [1 point] Is there a matrix that is both strictly upper and strictly lower triangular?
(Explain why not or else give an example of one.)
Solut
MA1s1-tut10 - Sage
07/12/2013 13:34
MA1s1-tut10
Problem 1
i) [2 points] We first define the variables for our system of linear equations.
var('x1,x2,x3,x4')
(x1, x2, x3, x4)
We define a system of equa
1S11 (McLoughlin) Tutorial sheet 5
[Week 6, 2012]
Name: Solutions
1. Write out a system of linear equations (in the unknowns x1 , x2 and x3 ) corresponding to
the augmented matrix:
2 4
3 : 2
7 0 1 :
1S11 (McLoughlin) Tutorial sheet 2
[Week 3, 2013]
Name: Solutions
1.
(a) Show (on the graph) the point P with coordinates (1, 3, 2) and the point Q with
coordinates (3, 2, 4).
(b) Sketch the position
1S11 (McLoughlin) Tutorial Solution sheet 6
[Week 8, 2013]
1. Find all solutions of the following system of linear equations by using Gauss-Jordan elimination. (Follow the method exactly.)
4x1 + 2x2 +
MA1S11 (McLoughlin) Tutorial/Exercise sheet 1
[due week 2, 2013]
Solutions
Each subquestion is worth 2 marks.
1. Consider the two-dimensional plane with the usual coordinate axes x and y
(a) Show (on
Mathematics for Scientists
MA1S1
Tristan McLoughlin
trist[email protected]
MA1S11
This course will cover various aspects of mathematics with a particular
focus on the tools, techniques and methods that
Vectors IV
MA1S1
Tristan McLoughlin
October 12, 2013
Anton & Rorres: Ch 3.4, 3.5
Heeron: Ch One, sec II.1 and II.2
Cross products
Denition: The cross product v w of two vectors
v
=
v1 i + v2 j + v3 k,
Vectors IV
MA1S1
Tristan McLoughlin
October 16, 2013
Anton & Rorres: Ch 3.4, 3.5
Heeron: Ch One, sec II.1 and II.2
Cross products
We previously described the the scalar product which takes two vectors
Matrices VI-VII
MA1S1
Tristan McLoughlin
November 21, 2013
Anton & Rorres: Ch 1.5, 1.6, 1.7, 10.6
Special matrices
There are matrices that have a special form that makes calculations with
them much ea
Graph Theory
MA1S1
Tristan McLoughlin
November 27, 2013
Anton & Rorres: 10.6
Robin J. Wilson: Introduction to Graph theory
Graph Theory
Recall some denitions (actually we will be a bit more general th
Number Systems
MA1S1
Tristan McLoughlin
November 27, 2013
http:/en.wikipedia.org/wiki/Binary numeral system
http:/accu.org/index.php/articles/1558
http:/www.binaryconvert.com
http:/en.wikipedia.org/wi
Matrices V
MA1S1
Tristan McLoughlin
November 15, 2013
Anton & Rorres: Ch 1.3, 1.4, 1.5
Elementary matrices
We now make a link between elementary row operations and matrix
multiplication.
Recall now th
Matrices - Sage
31/10/2013 21:06
Matrices
Dealing with matrices in SAGE is straightforward. We can
define a matrix with the Matrix() command and then specify the
entries as a list of of rows.
To creat
Linear Algebra II & III
MA1S1
Tristan McLoughlin
October 24, 2013
Anton & Rorres: Ch 1.1, 1.2, 1.9
Heeron: Ch One, sec I.1, sec III.3
Solving systems of equations, Gaussian elimination
We will now go
Linear Algebra I
MA1S1
Tristan McLoughlin
October 18, 2013
Anton & Rorres: Ch 1.1, 1.2
Heeron: Ch One, sec I.1
What is linear and not linear?
Here are some examples of equations that are plausibly int
Vectors II
MA1S1
Tristan McLoughlin
[email protected]
Anton & Rorres: Ch 3, sec 1 and 2
Heeron: Ch One, sec II.1 and II.2
Vectors - Review
We introduced the notion of a vector, a quantity with magn
Vectors III
MA1S1
Tristan McLoughlin
October 9, 2013
Anton & Rorres: Ch 3.3
Heeron: Ch One, sec II.1 and II.2
Dot product
The dot product of two 3-dimensional vectors v and w is given in terms
of the
Number Systems III
MA1S1
Tristan McLoughlin
December 4, 2013
http:/en.wikipedia.org/wiki/Binary numeral system
http:/accu.org/index.php/articles/1558
http:/www.binaryconvert.com
http:/en.wikipedia.org