Matrix Operations 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 are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns', indicating the number of rows and the number of columns.

Front

Can two matrices be added?

Back

Two matrices can be added if and only if they have the same dimensions.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, and the resulting matrix's dimensions depend on the dimensions of the two matrices being multiplied.

Front

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

Back

The result is a 2x2 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 does it mean for a matrix to be invertible?

Back

A matrix is invertible if there exists another matrix such that their product is the identity matrix.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix and provides information about the matrix, such as whether it is invertible.

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns.