Download presentation

Presentation is loading. Please wait.

1
MA10210: ALGEBRA 1B http://people.bath.ac.uk/aik22/ma10210

2
Comments on Sheet 6 Dont confuse dimension and rank Theyre closely related but not the same: A vector space has dimension. A map has rank. Neither is cardinality, so dont use the notation |V| Not every map is surjective

3
Comments on Sheet 7 Q6 – this question is asking for an alternative proof to Prop. 4.1.2: If we allow use of 4.1.2, theres nothing left in the question. The hints suggest an alternative method. Dont divide by something that might be zero: show its not zero first In a field, ab0 is enough to show that neither a nor b is zero.

4
Warm-up Question Q1: Find determinant by expanding about a row Find determinant by expanding about a column (Check theyre the same) Find the inverse Matrix of minors Cof(A) Adj(A) A -1

5
Find the determinants

6
Overview of Sheet 8 Q2: similar to Q1 Q3: A invertible if det A 0 Q4: put in matrix form, use notes on Cramers rule Q5(i): use hint; Q5(ii): note that A is invertible if and only if the columns of A are a basis.

7
Overview of Sheet 8 Q6(i): the determinant is zero if two (or more) rows are equal. When are two rows equal? Consider the determinant as a polynomial in x, y, z. What is the degree of this polynomial? Q6(ii): find the link to Q6(i), writing the system in matrix form Q6(iii): use some of the ideas from Q6(i)

Similar presentations

OK

Matrices CHAPTER 8.1 ~ 8.8. Ch8.1-8.8_2 Contents 8.1 Matrix Algebra 8.1 Matrix Algebra 8.2 Systems of Linear Algebra Equations 8.2 Systems of Linear.

Matrices CHAPTER 8.1 ~ 8.8. Ch8.1-8.8_2 Contents 8.1 Matrix Algebra 8.1 Matrix Algebra 8.2 Systems of Linear Algebra Equations 8.2 Systems of Linear.

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google