Nullity of a Matrix: Find the Answer

  • Context: Undergrad 
  • Thread starter Thread starter student444
  • Start date Start date
  • Tags Tags
    Matrix
Click For Summary
SUMMARY

The discussion centers on determining the nullity of a matrix with five columns, where one column consists entirely of zeros, and two columns contain leading ones. The user initially believes the nullity to be 3, referencing a textbook, but questions whether the correct nullity should be 2 based on the dimension of the null space. The confusion arises from the relationship between linear dependence and nullity, which is clarified by the need for more specific details about the matrix structure.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically nullity and null space.
  • Familiarity with matrix representation and column operations.
  • Knowledge of linear dependence and independence in vector spaces.
  • Ability to interpret mathematical problems from textbooks accurately.
NEXT STEPS
  • Study the definition and calculation of nullity in linear algebra.
  • Learn about the relationship between the rank and nullity of a matrix.
  • Explore examples of matrices with varying structures to practice determining null spaces.
  • Review resources on linear dependence and independence, focusing on their implications for matrix dimensions.
USEFUL FOR

Students and educators in mathematics, particularly those studying linear algebra, as well as anyone involved in mathematical problem-solving related to matrix theory.

student444
Messages
1
Reaction score
0
Hello.

A matrix has 5 columns.

One of the columns is all zeros.

Two of the columns have leading ones.

So the remaining 2 are linearly dependent in the matrix.

My question is. What is the nullity of the matrix?

My book would say 3 BUT the dimension of the null space is this matrix is 2 right?

So shouldn't the nullity be 2?

Thanks
 
Physics news on Phys.org
student444 said:
Hello.

A matrix has 5 columns.

One of the columns is all zeros.

Two of the columns have leading ones.

So the remaining 2 are linearly dependent in the matrix.

My question is. What is the nullity of the matrix?

My book would say 3 BUT the dimension of the null space is this matrix is 2 right?

So shouldn't the nullity be 2?

Thanks


It's hard to understand what you really mean, in particular because of that odd "so" and what follows in the 4th row.

Why don't you better post the actual matrix or at least tell us what book is that and in what page is the problem?

DonAntonio
 

Similar threads

Undergrad Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
3K
MHB Check the statements about a 4x5 matrix with rank 2.
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Find the parameter values that make ##L## surjective
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Confused about small detail in rank-nullity theorem
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Matrix diagonalization algorithm
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
  • · Replies 12 ·
Replies
12
Views
5K
Undergrad Proof concerning the Four Fundamental Spaces
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Are the columns space and row space same for idempotent matrix?
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K