Matrices

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that is a function of the entries of a square matrix and provides important properties of the matrix, such as whether it is invertible.

Front

What does it mean for a matrix to be invertible?

Back

A matrix is invertible if there exists another matrix such that their product is the identity matrix.

Front

What is Cramer's Rule?

Back

Cramer's Rule is a mathematical theorem used to solve a system of linear equations with as many equations as unknowns, using determinants.

Front

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

Back

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

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, denoted as I.

Front

What is a system of linear equations?

Back

A system of linear equations is a collection of one or more linear equations involving the same variables.

Front

What is the role of the coefficient matrix in a system of equations?

Back

The coefficient matrix contains the coefficients of the variables in the system of linear equations.

Front

What does it mean for a matrix to have no inverse?

Back

A matrix has no inverse if its determinant is zero, indicating that it is singular.

Front

How do you solve a system of equations using matrix inverses?

Back

To solve a system using matrix inverses, express the system in matrix form Ax = b, then find x = A^(-1)b.