Determinant in Mathematics
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Questions and Answers

What is the determinant of a 2 × 2 matrix with entries a, b, c, and d?

  • $ab - cd$
  • $ad - bc$ (correct)
  • $ac - bd$
  • $a + d - b - c$

    • Which formula expresses the determinant as a sum of n signed products of matrix entries?

  • Laplace expansion
  • Cramer's rule
  • Leibniz formula (correct)
  • Gaussian elimination

    • When is the determinant of a matrix nonzero?

  • When the matrix is invertible (correct)
  • When the matrix is skew-symmetric
  • When the matrix is singular
  • When the matrix is symmetric

    • How can the determinant of an n × n matrix be computed using a method that expresses it as a linear combination of determinants of submatrices?

    <p>Laplace expansion</p> Signup and view all the answers

    What is the determinant of a 3 × 3 matrix with entries a, b, c, d, e, f, g, h, and i?

    <p>$aei+bfg+cdh-ceg-bdi-afh$</p> Signup and view all the answers

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