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Questions and Answers
What is the maximum number of linearly independent vectors in a set of vectors in ℝⁿ?
What is the maximum number of linearly independent vectors in a set of vectors in ℝⁿ?
- infinite
- n+1
- n (correct)
- n-1
If A is an n × n matrix, then which of the following is true?
If A is an n × n matrix, then which of the following is true?
- A is invertible if and only if its determinant is non-zero (correct)
- determinant of A is always zero
- A is singular if and only if its rank is n
- trace of A is always zero
Let A be an n × n matrix. The Cayley-Hamilton theorem states that:
Let A be an n × n matrix. The Cayley-Hamilton theorem states that:
- A satisfies its characteristic equation (correct)
- A is singular
- A is diagonalizable
- A is invertible
Let A be an m × n matrix and let T: ℝⁿ → ℝᵐ be the linear transformation defined by T(x) = Ax. What is the rank of A?
Let A be an m × n matrix and let T: ℝⁿ → ℝᵐ be the linear transformation defined by T(x) = Ax. What is the rank of A?
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What is the relation between the rank and nullity of a matrix A?
What is the relation between the rank and nullity of a matrix A?
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