AA C&C Unit 5 FLASHCARD: Matrix Operations

The inverse of a matrix A is another matrix, denoted as A^(-1), such that when A is multiplied by A^(-1), the result is the identity matrix I. That is, AA^(-1) = A^(-1)A = I.

Two matrices A and B are inverses if and only if AB = I and BA = I, where I is the identity matrix.

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. For a 2x2 matrix, it is represented as $$I_2 = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$$ .

The determinant of matrix A is calculated as det(A) = ad - bc.

If the determinant of a matrix is zero, it means that the matrix is singular and does not have an inverse.

The inverse of matrix A is given by $$A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \ -c & a \end{pmatrix}$$ , provided that the determinant (ad - bc) is not zero.

A coefficient matrix is a matrix that contains the coefficients of the variables in a system of linear equations.

For a 2x2 matrix $$A = \begin{pmatrix} a & b \ c & d \end{pmatrix}$$ , the determinant is calculated as det(A) = ad - bc.

The result of adding two matrices A and B is a new matrix C, where each element C[i][j] = A[i][j] + B[i][j], provided A and B have the same dimensions.

The result of subtracting matrix A from matrix B is a new matrix C, where each element C[i][j] = B[i][j] - A[i][j], provided A and B have the same dimensions.