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Questions and Answers
What does the rank of a matrix represent?
What does the rank of a matrix represent?
- Dimension of the image of the matrix (correct)
- Trace of the matrix
- Dimension of the kernel of the matrix
- Determinant of the matrix
Which property does the nullity of a matrix refer to?
Which property does the nullity of a matrix refer to?
- Determinant of the matrix
- Trace of the matrix
- Dimension of the kernel of the matrix (correct)
- Dimension of the image of the matrix
In the context of matrices, what does 'dim(im A)' stand for?
In the context of matrices, what does 'dim(im A)' stand for?
- Dimension of the kernel of the matrix
- Determinant of the matrix
- Dimension of the image of the matrix (correct)
- Trace of the matrix
How do you determine the nullity of an n × m matrix A?
How do you determine the nullity of an n × m matrix A?
What does the rank of an n × m matrix A represent?
What does the rank of an n × m matrix A represent?
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?
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?
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?
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?
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