Matrices Basics Flashcard

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What does the notation r_ij represent in a matrix?

Back

r_ij represents the element located in the i-th row and j-th column of a matrix.

Front

How do you determine the dimensions of a matrix?

Back

The dimensions of a matrix are given by the number of rows and columns it contains, expressed as 'rows x columns'.

Front

What is the result of adding two matrices?

Back

The result is a new matrix where each element is the sum of the corresponding elements from the two matrices, provided they have the same dimensions.

Front

What is the result of subtracting two matrices?

Back

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

Front

What is the identity matrix?

Back

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

Front

How do you find the transpose of a matrix?

Back

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