Matrices (Operations & Determinants) Flashcard

Front

What is a matrix?

Back

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

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'm x n', where 'm' is the number of rows and 'n' is the number of columns.

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 matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, and is only defined when the number of columns in the first matrix equals the number of rows in the second.

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 about the matrix.

Front

How do you find 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 a scalar matrix?

Back

A scalar matrix is a square matrix in which all the elements of the principal diagonal are equal and all other elements are zero.

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.