Linear Algebra: Nullity of Matrix Product Question

In summary, linear algebra is a branch of mathematics that focuses on the study of linear equations, matrices, and vector spaces. Its purpose is to provide a framework for solving problems involving linear relationships and it has various applications in fields such as computer science, physics, engineering, and economics. Some common operations in linear algebra include matrix multiplication, vector addition and subtraction, finding determinants and eigenvalues, and solving systems of linear equations. It is used in real life for tasks such as image and signal processing, data analysis, machine learning, and computer graphics. There are many resources available for learning linear algebra, including textbooks, online courses, and video tutorials. Some popular textbooks include "Linear Algebra and Its Applications" by David C. Lay and "
  • #1
workerant
41
0
Prove that for any m*n matrix A and any n*n matrix B, nullity A is less than or equal to nullity AB.

Sorry Dick: I know nullity of A is n-rank A and this is always greater than or equal to 0 and I figured nullity AB is like nullity A * nullity B, which are both greater than or equal to 0. Is this in the right direction?
 
Last edited:
Physics news on Phys.org
  • #2
Any thoughts on this? Even if you have no idea how to solve it you are supposed to at least thrash around and show an attempt. Such are the forum rules.
 

1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations, matrices, and vector spaces. It involves the manipulation and analysis of linear relationships between variables.

2. What is the purpose of linear algebra?

The purpose of linear algebra is to provide a framework for solving mathematical problems involving linear relationships. It also has various applications in fields such as computer science, physics, engineering, and economics.

3. What are some common operations in linear algebra?

Some common operations in linear algebra include matrix multiplication, vector addition and subtraction, finding determinants and eigenvalues, and solving systems of linear equations.

4. How is linear algebra used in real life?

Linear algebra has numerous applications in real life, such as image and signal processing, data analysis, machine learning, and computer graphics. It is also used in engineering for solving problems related to circuits and structures.

5. What are some resources for learning linear algebra?

There are many resources available for learning linear algebra, including textbooks, online courses, and video tutorials. Some popular textbooks include "Linear Algebra and Its Applications" by David C. Lay and "Introduction to Linear Algebra" by Gilbert Strang. Khan Academy and MIT OpenCourseWare also offer free online courses on linear algebra.

Similar threads

Finding properties of a linear transformation
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Finding Kernel, Image, Rank, Nullity of Matrix
    • Calculus and Beyond Homework Help
Replies
1
Views
926
I don't understand why the rank = n - Rank-nullity theorem - nullity
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Rank of A & Construction of W: Linear Algebra Homework
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Full Rank Matrix: Determinant Condition | Rank-Nullity Theorem
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Proving a statement about the rank of transformations
    • Calculus and Beyond Homework Help
Replies
11
Views
1K
Proving Nullity in Linear Algebra: A < AB for m*n and n*n Matrices
    • Calculus and Beyond Homework Help
Replies
1
Views
3K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
    • Calculus and Beyond Homework Help
Replies
14
Views
590
Write a matrix given the null space
    • Calculus and Beyond Homework Help
Replies
10
Views
4K
Linear maps (rank and nullity)
    • Calculus and Beyond Homework Help
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top