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 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 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

When does a matrix have 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

How do you find 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 matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, following specific rules.