Matrix Quiz

A matrix is defined by its dimensions in the format 'rows x columns'. Here, there are 3 rows and 4 columns, so the correct size of the matrix is 3x4.

In an m x n matrix, 'm' denotes the number of rows. The first dimension represents rows, while 'n' represents columns. Therefore, the correct answer is 'The number of rows'.

A matrix with the same number of rows and columns is called a square matrix. This distinguishes it from row, column, and rectangular matrices, which do not have equal dimensions.

The (2,3) entry refers to the element in the 2nd row and 3rd column of the matrix. In the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]], this corresponds to the number 6.

A row vector is defined as a matrix with one row and multiple columns. This means it has a single horizontal arrangement of elements, making the correct choice 'One row and multiple columns'.

A column vector is defined as a matrix with multiple rows and one column, making 'Multiple rows and one column' the correct choice. The other options describe different matrix configurations.

Two matrices A and B are equal if they have the same size (same number of rows and columns) and all corresponding entries are equal. Thus, the correct choice is that they have the same size and corresponding entries are equal.

To multiply matrices, the number of columns in the first matrix (A, 3 columns) must equal the number of rows in the second matrix (B, 3 rows). The resulting matrix AB will have the dimensions of the outer matrices: 2 rows from A and 4 columns from B, resulting in a 2x4 matrix.

Matrix addition is defined only for matrices of the same size, meaning they must have the same number of rows and columns. This ensures that corresponding elements can be added together, making 'the same size' the correct choice.

The sum of two matrices A and B is defined only when they have the same dimensions. Since both A and B are m x n matrices, their sum A + B will also be an m x n matrix.