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 (C)</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 (D)</p> Signup and view all the answers

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