AA C&C Unit 5 FLASHCARD: Matrix Operations

Front

What is the definition of matrix inverse?

Back

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.

Front

How do you determine if two matrices A and B are inverses?

Back

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

Front

What is the identity matrix?

Back

Front

Back

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

Front

What does it mean if the determinant of a matrix is zero?

Back

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

Front

Back

Front

What is a coefficient matrix?

Back

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

Front

How do you calculate the determinant of a 2x2 matrix?

Back

Front

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

Back

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.

Front

What is the result of subtracting matrix A from matrix B?

Back

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.