9 Questions
What does the rank of a matrix represent?
Dimension of the image of the matrix
Which property does the nullity of a matrix refer to?
Dimension of the kernel of the matrix
In the context of matrices, what does 'dim(im A)' stand for?
Dimension of the image of the matrix
How do you determine the nullity of an n × m matrix A?
By counting the number of free variables
What does the rank of an n × m matrix A represent?
The dimension of the image of A
In the context of matrices, what is the relationship between the nullity and the rank?
The rank minus the nullity is equal to n
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?
The kernel of A must be of dimension 1.
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?
[0 1 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?
Matrix A must have linearly dependent rows/columns.
Learn about the concepts of matrix rank and nullity, where the rank is the dimension of the image of the matrix and the nullity is the dimension of the kernel of the matrix. Understand how these concepts are related to the properties and transformations of matrices.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
