Matrices - Determinants and Inverses

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 the determinant of a 2x2 matrix?

Back

The determinant of a 2x2 matrix is calculated using the formula ad - bc, where the matrix is represented as [[a, b], [c, d]].

Front

What does it mean if a matrix has no inverse?

Back

A matrix has no inverse if its determinant is zero, indicating that it is singular and does not span the entire space.

Front

How do you find the inverse of a 2x2 matrix?

Back

To find the inverse of a 2x2 matrix [[a, b], [c, d]], use the formula (1/det) * [[d, -b], [-c, a]], where det = ad - bc.

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 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 the formula for the determinant of a 3x3 matrix?

Back

The determinant of a 3x3 matrix can be calculated using the rule of Sarrus or cofactor expansion.

Front

What is the relationship between a matrix and its inverse?

Back

A matrix A and its inverse A^-1 satisfy the equation A * A^-1 = I, where I is the identity matrix.

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

How can you determine if a matrix is invertible?

Back

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