Matrix Addition, Subtraction, Multiplication, & Determinant

Front

What is the definition of a matrix?

Back

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

Front

What is matrix addition?

Back

Matrix addition is the operation of adding two matrices by adding their corresponding elements.

Front

What is matrix subtraction?

Back

Matrix subtraction is the operation of subtracting one matrix from another by subtracting their corresponding elements.

Front

What is matrix multiplication?

Back

Matrix multiplication is the operation of multiplying two matrices by taking the dot product of 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 of 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 the formula for the determinant of a 3x3 matrix?

Back

For a 3x3 matrix [[a, b, c], [d, e, f], [g, h, i]], the determinant is a(ei - fh) - b(di - fg) + c(dh - eg).

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 zero matrix?

Back

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

Front

What is the commutative property of matrix addition?

Back

The commutative property states that A + B = B + A for any matrices A and B of the same dimensions.