Determinant Mastery

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Questions and Answers

What is the determinant of a 2 × 2 matrix?

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

What does a nonzero determinant of a matrix indicate?

The matrix is singular.
The matrix is symmetric.
The matrix is diagonal.
The matrix is invertible. (correct)

Which of the following is a correct statement about the determinant?

The determinant of a matrix A characterizes the properties of the linear map represented by the matrix.
The determinant of a matrix A is always zero.
The determinant of a matrix A is the sum of its entries.
The determinant of a matrix A is denoted as det(A), det A, or |A|. (correct)

What is the determinant of a 3 × 3 matrix?

<p>$|a b c d e f g h i| = aei + bfg + cdh - ceg - bdi - afh$ (B)</p> Signup and view all the answers

How can the determinant of an n × n matrix be defined?

<p>Leibniz formula (A)</p> Signup and view all the answers

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Study Notes

What is the determinant of a 2 × 2 matrix? What does a nonzero determinant of a matrix indicate? Which of the following is a correct statement about the determinant? What is the determinant of a 3 × 3 matrix? How can the determinant of an n × n matrix be defined?