Podcast
Questions and Answers
What does the rank of a matrix represent?
What does the rank of a matrix represent?
Which property does the nullity of a matrix refer to?
Which property does the nullity of a matrix refer to?
In the context of matrices, what does 'dim(im A)' stand for?
In the context of matrices, what does 'dim(im A)' stand for?
How do you determine the nullity of an n × m matrix A?
How do you determine the nullity of an n × m matrix A?
Signup and view all the answers
What does the rank of an n × m matrix A represent?
What does the rank of an n × m matrix A represent?
Signup and view all the answers
In the context of matrices, what is the relationship between the nullity and the rank?
In the context of matrices, what is the relationship between the nullity and the rank?
Signup and view all the answers
If A and B are square matrices of size 3×3 and AB has a kernel of dimension 2, what can be said about the kernel of A?
If A and B are square matrices of size 3×3 and AB has a kernel of dimension 2, what can be said about the kernel of A?
Signup and view all the answers
What is a possible matrix B that, when multiplied by I (the identity matrix), would result in a product with a kernel of dimension 2?
What is a possible matrix B that, when multiplied by I (the identity matrix), would result in a product with a kernel of dimension 2?
Signup and view all the answers
If matrix B is square and contains non-zero elements, what property must matrix A have to ensure that the product AB has a kernel of dimension greater than 0?
If matrix B is square and contains non-zero elements, what property must matrix A have to ensure that the product AB has a kernel of dimension greater than 0?
Signup and view all the answers
