Matrices # 1

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 matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, resulting in a new matrix.

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 calculate 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 inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A⁻¹, such that when multiplied together, they yield 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]], 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 the result of adding two matrices?

Back

The result of adding two matrices is a new matrix where each element is the sum of the corresponding elements of the original matrices.

Front

What is the result of subtracting two matrices?

Back

The result of subtracting two matrices is a new matrix where each element is the difference of the corresponding elements of the original matrices.

Front

What does it mean for matrices to be compatible for addition?

Back

Matrices are compatible for addition if they have the same dimensions (same number of rows and columns).