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Questions and Answers
What is the determinant of a 2 × 2 matrix with entries a, b, c, and d?
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?
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 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?
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?
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What is the determinant of a 3 × 3 matrix with entries a, b, c, d, e, f, g, h, and i?
What is the determinant of a 3 × 3 matrix with entries a, b, c, d, e, f, g, h, and i?
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