Matrices Review for Final

Front

What is the dimension of a matrix?

Back

The dimension of a matrix is defined by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a matrix with 3 rows and 2 columns is a 3x2 matrix.

Front

How do you find the product of two matrices?

Back

To find the product of two matrices, multiply the rows of the first matrix by the columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimension. The result is a new matrix of the same dimension.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that when A is multiplied by A^-1, the result is the identity matrix. Not all matrices have inverses.

Front

What is an identity matrix?

Back

An 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 elements are zero. It serves as the additive identity in matrix addition.

Front

What is a square matrix?

Back

A square matrix is a matrix with the same number of rows and columns, such as a 2x2 or 3x3 matrix.

Front

What is a row matrix?

Back

A row matrix is a matrix that has only one row and multiple columns, such as 1x3.

Front

What is a column matrix?

Back

A column matrix is a matrix that has only one column and multiple rows, such as 3x1.

Front

What is a determinant of a matrix?

Back

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