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 inverse of a matrix?

Back

To find the inverse of a matrix A, you can use the formula A^(-1) = (1/det(A)) * adj(A), where det(A) is the determinant and adj(A) is the adjugate of A.

Front

What is the formula for 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 0?

Back

If the determinant of a matrix is 0, it means that the matrix is singular and does not have an inverse.

Front

What is an identity matrix?

Back

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

Front

How can you determine if a matrix is invertible?

Back

A matrix is invertible if its determinant is non-zero.

Front

What is the adjugate of a matrix?

Back

The adjugate of a matrix is the transpose of its cofactor matrix, used in calculating the inverse of the matrix.

Front

What is a cofactor in a matrix?

Back

A cofactor is the signed minor of an element in a matrix, calculated by deleting the row and column of that element.

Front

How do you calculate the determinant of a 3x3 matrix?

Back

For a 3x3 matrix, the determinant can be calculated using the rule of Sarrus or by expansion of minors.