Inverse Matrix

Front

What is an inverse matrix?

Back

An inverse matrix is a matrix that, when multiplied by the original matrix, results in 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 a determinant?

Back

The determinant is a scalar value that is a function of a square matrix, providing important properties of the matrix.

Front

How do you find 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 if the determinant of a matrix is zero?

Back

If the determinant is zero, the matrix does not have an inverse and is called singular.

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.

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, often because its determinant is zero.

Front

What is the relationship between a matrix and its inverse?

Back

A matrix multiplied by its inverse equals the identity matrix.

Front

Can all matrices have inverses?

Back

No, only square matrices with a non-zero determinant have inverses.

Front

What is the effect of multiplying a matrix by its inverse?

Back

Multiplying a matrix by its inverse results in the identity matrix.