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 matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions.

Front

What is matrix subtraction?

Back

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

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 of the matrix.

Front

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

Back

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

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that AA^-1 = I, where I is the identity matrix.

Front

When does a matrix have an inverse?

Back

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

Front

What is an identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero.

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns.