Matrices - Determinants and Inverses

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that is a function of the entries of a square matrix, providing important properties such as whether the matrix is invertible.

Front

How do you find the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.

Front

What does it mean if the determinant of a matrix is zero?

Back

If the determinant is zero, the matrix is singular, meaning it does not have an inverse.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that when multiplied with A, it yields the identity matrix.

Front

How can you determine if a matrix has an inverse?

Back

A matrix has an inverse if and only if its determinant is non-zero.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, denoted as I.

Front

What is the formula for finding the inverse of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the inverse is (1/det(A)) * [[d, -b], [-c, a]], where det(A) = ad - bc.

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, typically because its determinant is zero.

Front

What is the cofactor of an element in a matrix?

Back

The cofactor of an element is the signed determinant of the submatrix formed by deleting the row and column of that element.