Determinants and Inverses of Matrices

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A⁻¹, such that when A is multiplied by A⁻¹, the result is the identity matrix I. Not all matrices have inverses.

Front

How do you calculate 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 condition for a matrix to have an inverse?

Back

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

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. For a 2x2 matrix, it is ⌈1 & 0⌉
⌊0 & 1⌋.

Front

What must be true in order to add two matrices?

Back

The dimensions of the two matrices must be equal.

Front

What is the result of adding two matrices A and B?

Back

The result is a new matrix where each element is the sum of the corresponding elements of A and B.

Front

What is the product of two matrices?

Back

The product of two matrices A and B is a new matrix C, where each element C[i][j] is the sum of the products of the elements of the i-th row of A and the j-th column of B.

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, which occurs when its determinant is zero.

Front

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

Back

For a 2x2 matrix ⌈a & b⌉
⌊c & d⌋, the inverse is given by (1/det) * ⌈d & -b⌉
⌊-c & a⌋, where det = ad - bc.

Front

What is the determinant of the matrix ⌈4 & -3⌉
⌊12 & 3⌋?

Back

The determinant is calculated as (4)(3) - (-3)(12) = 12 + 36 = 48.