Matrix Review

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. It provides important information about the matrix, such as whether it 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 is matrix multiplication?

Back

Matrix multiplication is an operation that takes two matrices and produces a third matrix by multiplying rows of the first matrix by columns of the second.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in terms of rows and columns, expressed as 'm x n' where m is the number of rows and n is the number of columns.

Front

How do you find the inverse of a matrix?

Back

The inverse of a matrix A is denoted as A^-1 and is found such that A * A^-1 = I, where I is the identity matrix. Not all matrices have inverses.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all the elements are zero. It serves as the additive identity in matrix addition.

Front

What is the significance of a matrix having a determinant of zero?

Back

If a matrix has a determinant of zero, it is singular, meaning it does not have an inverse and its rows (or columns) are linearly dependent.

Front

How do you perform matrix addition?

Back

Matrix addition is performed by adding corresponding elements of two matrices of the same dimensions.

Front

What is a row matrix?

Back

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