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 multiplication?

Back

Matrix multiplication involves taking the dot product of rows and columns of two matrices, where the number of columns in the first matrix must equal the number of rows in the second.

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 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 an identity matrix?

Back

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

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 together, they yield the identity matrix: AA^-1 = I.

Front

What are the properties of matrix addition?

Back

Matrix addition is commutative (A + B = B + A) and associative ((A + B) + C = A + (B + C)).

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, denoted as A^T.