Matrices - Determinants and Inverses

Front

What is a matrix?

Back

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

Front

What is the determinant of a 2x2 matrix?

Back

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

Front

What does it mean for a matrix to have an inverse?

Back

A matrix has an inverse if there exists another matrix such that their product 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

How do you determine if a matrix is invertible?

Back

A matrix is invertible if its determinant is non-zero.

Front

What is the determinant of the matrix [[1, 2], [3, 4]]?

Back

The determinant is (1*4) - (2*3) = 4 - 6 = -2.

Front

What is the size of a matrix?

Back

The size of a matrix is defined by the number of rows and columns it contains, expressed as rows x columns.

Front

What is a 3x2 matrix?

Back

A 3x2 matrix has 3 rows and 2 columns.

Front

Can a 2x3 matrix have an inverse?

Back

No, a 2x3 matrix cannot have an inverse because it is not square.

Front

What is the formula for finding 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.