Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What does it mean to add two matrices?

Back

To add two matrices, they must have the same dimensions (same number of rows and columns). The corresponding elements are added together.

Front

What is the condition for matrix addition?

Back

Matrices can only be added if they have the same number of rows and columns.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that when A is multiplied by A^-1, the result is the identity matrix.

Front

What is the identity matrix?

Back

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

Front

What does it mean if a matrix has no inverse?

Back

A matrix has no inverse if it is singular, meaning its determinant is zero.

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) * [[d, -b], [-c, a]], where det = ad - bc.

Front

What is a determinant?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix and provides information about the matrix, such as whether it is invertible.

Front

What is the formula for the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is 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.