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

Lecture 10 Dimensions, Independence, Basis and Complete Solution of Linear Systems Shang-Hua Teng.

Lecture 10 Dimensions, Independence, Basis and Complete Solution of Linear Systems Shang-Hua Teng.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on understanding by design Ppt on stock exchanges in india Free ppt on balanced diet Moral values for kids ppt on batteries Ppt on human nutrition and digestion worksheet Ppt on classical economics school Ppt on polynomials and coordinate geometry calculator Ppt on high level languages examples Ppt on social media on business Ppt on holographic data storage system technology