Review of Inverse Matrices

Front

What is an inverse matrix?

Back

An inverse matrix A^-1 of a matrix A is a matrix such that when multiplied with A, it yields the identity matrix I (A * A^-1 = I).

Front

How do you determine if a matrix has an inverse?

Back

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

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 is the formula for finding the inverse of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the inverse is given by (1/det(A)) * [[d, -b], [-c, a]], where det(A) = ad - bc.

Front

What does it mean if a matrix has no inverse?

Back

If a matrix has no inverse, it is called a singular matrix, which occurs when its determinant is zero.

Front

Calculate the determinant of the matrix [[6, 4], [3, 2]].

Back

The determinant is (6*2) - (4*3) = 12 - 12 = 0.

Front

Does the matrix [[6, 4], [3, 2]] have an inverse?

Back

No, because its determinant is zero.

Front

Find the inverse of the matrix [[1, 2], [3, 4]].

Back

The inverse is (-2, 1), (1.5, -0.5).

Front

What is the identity matrix for 2x2 matrices?

Back

The identity matrix for 2x2 matrices is [[1, 0], [0, 1]].

Front

If A is a 2x2 matrix, what is the relationship between A and A^-1?

Back

A * A^-1 = I, where I is the identity matrix.