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

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 together?

Back

Yes, two matrices can be added together if they have the same dimensions.

Front

What is the result of subtracting two matrices of the same dimensions?

Back

The result is a new matrix where each element is the difference of the corresponding elements from the two matrices.

Front

What is an element of a matrix?

Back

An element of a matrix is an individual value or entry located at a specific position within the matrix.

Front

How do you denote the element in the i-th row and j-th column of a matrix A?

Back

It is denoted as A[i][j] or a_{ij}.

Front

What is the zero matrix?

Back

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

Front

What is the identity matrix?

Back

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

Front

What is matrix multiplication?

Back

Matrix multiplication is an operation that produces a new matrix by multiplying rows of the first matrix by columns of the second matrix.

Front

What are the conditions for matrix multiplication to be defined?

Back

Matrix multiplication is defined when the number of columns in the first matrix equals the number of rows in the second matrix.