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 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 does it mean for two matrices to be inverses of each other?

Back

Two matrices A and B are inverses if their product is the identity matrix, i.e., AB = I and BA = I.

Front

How do you find the inverse of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the inverse is given by (1/det(A)) * [[d, -b], [-c, a]], where det(A) = ad - bc.

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 defined?

Back

Matrix multiplication is defined when the number of columns in the first matrix equals the number of rows in the second matrix.

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 a scalar in the context of matrices?

Back

A scalar is a single number that can multiply a matrix, affecting all its elements.