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Questions and Answers
What is the primary purpose of calculating the rank of a matrix?
What is the primary purpose of calculating the rank of a matrix?
- To classify the type of matrix based on its dimensions
- To determine the number of non-zero rows in its echelon form (correct)
- To compute the inverse of the matrix
- To find the eigenvalues of the matrix
Which of the following properties is NOT true for eigenvectors of a matrix?
Which of the following properties is NOT true for eigenvectors of a matrix?
- Eigenvectors must always form a complete basis for the vector space. (correct)
- An eigenvector associated with an eigenvalue can be scaled by any non-zero scalar.
- Eigenvectors can be zero vectors only if the eigenvalue is zero.
- Eigenvectors corresponding to distinct eigenvalues are linearly independent.
What is the relationship between the adjoint of a matrix and its inverse?
What is the relationship between the adjoint of a matrix and its inverse?
- The adjoint represents only the diagonal elements of the inverse.
- The inverse is equal to the adjoint divided by the determinant. (correct)
- The adjoint can be calculated directly from the inverse.
- Both the adjoint and inverse yield the same matrix if the original is singular.
In how many ways can a matrix be classified based on its eigenvalues?
In how many ways can a matrix be classified based on its eigenvalues?
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Which of the following forms does NOT describe a type of normal form for matrices?
Which of the following forms does NOT describe a type of normal form for matrices?
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