
Understanding Matrices and Determinants in Algebra
Explore the concept of matrices and determinants in algebra through transformations, area calculations, and determinant properties. Learn about the significance of determinants, different transformations represented by matrices, and how to find determinants of various matrices. Dive into examples and explanations to grasp the fundamental concepts in linear algebra.
Download Presentation

Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Matrices: Determinants The unit square is transformed by the matrix ? ? ? ? Find the area of the new shape in terms of a, b, c and d.
Matrices: Determinants The area scale factor of the transformative matrix ? ? ? is ? ?? ??. This is called the determinant of the matrix.
Given that P = 2 1 1 and Q = 2 1 2, find 0 1 a) detP b) detQ c) det(PQ) Does the answer to part c make sense?
FP1 questions: June 2014 Q7ii June 2013R Q6a, b May 2017 Q5ii June 2011 Q5
Describe the transformation represented by the matrix 2 0 0 0 2 0 0 0 2 Use your calculator to work out the determinant of this matrix and explain its significance.
A matrix T maps all points on the line ? + 2? = 1 to the point (1,3). a) Find the matrix T and show that it has a determinant of zero. b) Show that T maps all points on the plane to the line ? = 3? c) Find the coordinate to which all points on the line ? + 2? = 3 are mapped.
The determinants of all the possible 2 by 2 matrices with elements between -5 and 5 (inclusive): Value of determinant