Matrices

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 and provides important properties of the matrix, such as whether it 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) = adj(A)/det(A), where adj(A) is the adjugate of A and det(A) is the determinant of A.

Front

What does it mean if a matrix has no inverse?

Back

A matrix has no inverse if its determinant is zero, indicating that it is singular and does not span the entire space.

Front

What is Cramer's Rule?

Back

Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns, using determinants.

Front

How do you perform matrix addition?

Back

Matrix addition is performed by adding corresponding elements of two matrices of the same dimensions.

Front

What is matrix subtraction?

Back

Matrix subtraction is the operation of subtracting corresponding elements of two matrices of the same dimensions.

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, and it acts as the multiplicative identity in matrix multiplication.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns, denoted as A^T.

Front

What is a square matrix?

Back

A square matrix is a matrix with the same number of rows and columns.