Matrices Review

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What is the determinant of a 2x2 matrix A = ⌈a & b⌉
⌊c & d⌋?

Back

The determinant is calculated as det(A) = ad - bc.

Front

How do you find the inverse of a 2x2 matrix A = ⌈a & b⌉
⌊c & d⌋?

Back

The inverse is given by A⁻¹ = (1/det(A)) * ⌈d & -b⌉
⌊-c & a⌋, provided det(A) ≠ 0.

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 product of two matrices?

Back

The product of two matrices is obtained by multiplying rows of the first matrix by columns of the second matrix.

Front

What does it mean for two matrices to be multiplicative inverses?

Back

Two matrices A and B are multiplicative inverses if AB = I, where I is the identity matrix.

Front

What is the zero matrix?

Back

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

Front

How do you add two matrices?

Back

You add two matrices by adding their corresponding elements.

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 swapping its rows and columns.