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Questions and Answers
What is the purpose of the rank-nullity theorem?
What is the purpose of the rank-nullity theorem?
- To determine the number of pivot columns in a matrix
- To determine the solvability of a system of linear equations (correct)
- To find the eigenvalues of a matrix
- To evaluate the inverse of a matrix
What do eigenvalues and eigenvectors represent?
What do eigenvalues and eigenvectors represent?
- Pivot columns and row echelon form of a matrix
- Rank and nullity of a matrix
- Scale factors and directions of a matrix transformation (correct)
- Inverse and determinant of a matrix
What is the Cayley-Hamilton theorem used for?
What is the Cayley-Hamilton theorem used for?
- To prove that every matrix is diagonalizable
- To find the eigenvalues of a matrix
- To find the determinant of a matrix
- To express the powers of a matrix in terms of its eigenvalues (correct)
What is the primary application of the inverse by partitioning method?
What is the primary application of the inverse by partitioning method?
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What is the relationship between the rank of a matrix and its nullity?
What is the relationship between the rank of a matrix and its nullity?
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