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

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 the determinant of a 3x3 matrix?

Back

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

Front

What does it mean for two matrices to be inverses of each other?

Back

Two matrices A and B are inverses if AB = BA = I, where I 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 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

How do you calculate the determinant of a 3x3 matrix?

Back

To calculate the determinant of a 3x3 matrix, use the formula: det(A) = a(ei-fh) - b(di-fg) + c(dh-eg).

Front

What is the relationship between determinants and inverses?

Back

A matrix has an inverse if and only if its determinant is non-zero.