Matrices Review

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 is an operation that produces a new matrix by multiplying rows of the first matrix by columns of the second matrix.

Front

What are the conditions for matrix multiplication?

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 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 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 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 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.

Front

What is a scalar in matrix operations?

Back

A scalar is a single number that can multiply a matrix, affecting each element of the matrix.

Front

What is a row matrix?

Back

A row matrix is a matrix that has only one row and multiple columns.