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 condition for multiplying two matrices A and B?

Back

Matrices A and B can be multiplied if the number of columns in A is equal to the number of rows in B.

Front

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

Back

The determinant of matrix A is calculated as det(A) = 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 AA⁻¹ = I, where I is the identity matrix.

Front

How do you calculate 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 the identity matrix?

Back

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

Front

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

Back

Two matrices can be added if they have the same dimensions (same number of rows and columns).

Front

What is a zero matrix?

Back

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

Front

What is the transpose of a matrix?

Back

The transpose of a matrix A is obtained by flipping it over its diagonal, turning rows into columns.

Front

What is the product of a matrix and a zero matrix?

Back

The product of any matrix A and a zero matrix results in a zero matrix.