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 2x2 matrix?

Back

For a matrix A = [[a, b], [c, d]], the determinant is calculated as ad - bc.

Front

How do you find the inverse of a matrix?

Back

The inverse of a matrix A exists if and only if the determinant of A is non-zero. It can be found using the formula A^(-1) = (1/det(A)) * adj(A), where adj(A) is the adjugate of A.

Front

What does it mean if a matrix has no inverse?

Back

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

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions.

Front

What is matrix subtraction?

Back

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions.

Front

What is the product of two matrices?

Back

The product of two matrices A (m x n) and B (n x p) is a new matrix C (m x p) where each element is the dot product of the corresponding row of A and column of B.

Front

What is a square matrix?

Back

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

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero.

Front

What is a diagonal matrix?

Back

A diagonal matrix is a square matrix in which all elements outside the main diagonal are zero.