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Linear Algebra Quiz

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Questions and Answers

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?

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:

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?

<p>the dimension of the image of T</p> Signup and view all the answers

What is the relation between the rank and nullity of a matrix A?

<p>rank(A) + nullity(A) = number of columns of A</p> Signup and view all the answers

Linear Algebra Quiz

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Questions and Answers

What is the maximum number of linearly independent vectors in a set of vectors in ℝⁿ?

If A is an n × n matrix, then which of the following is true?

Let A be an n × n matrix. The Cayley-Hamilton theorem states that:

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?

What is the relation between the rank and nullity of a matrix A?

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