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, providing important properties such as whether the matrix is invertible.

Front

How do you evaluate 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 two matrices to be added?

Back

The dimensions of the two matrices must be equal.

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 not equal to zero.

Front

What is a square matrix?

Back

A square matrix is a matrix with the same number of rows and columns.

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 the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^(-1), such that AA^(-1) = I, where I is the identity matrix.

Front

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

Back

For a 2x2 matrix [[a, b], [c, d]], the inverse is (1/det(A)) * [[d, -b], [-c, a]], provided det(A) ≠ 0.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of equations with the same variables that can be solved simultaneously.