Matrices Flashcard for Adv. Alg.

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. Add corresponding elements from each matrix.

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

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have dimensions equal to the number of rows of the first matrix and the number of columns of the second matrix.

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

Front

What is the transpose of a matrix?

Back

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

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, providing important properties about the matrix, such as whether it is invertible.

Front

What does it mean for a matrix to be invertible?

Back

A matrix is invertible (or non-singular) if there exists another matrix such that their product is the identity 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 and sum the products.