Matrices review pre 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 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 are the conditions for matrix multiplication to be possible?

Back

The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is the determinant of a 2x2 matrix?

Back

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

Front

How do you calculate the determinant of a 3x3 matrix?

Back

The determinant of a 3x3 matrix can be calculated using the rule of Sarrus or cofactor expansion.

Front

What does it mean if the determinant of a matrix is zero?

Back

If the determinant is zero, the matrix is singular, meaning it does not have an inverse.

Front

What is an identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

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

What is a scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a constant number).

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal, switching the row and column indices.