Matrix Quiz

What is the size of a matrix with 3 rows and 4 columns?

• 4x3

• 3x4

• 7

• 12

Answer explanation

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, what does 'm' represent?

• The number of columns

• The number of entries

• The number of rows

• The size of the matrix

Answer explanation

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:

• Row matrix

• Column matrix

• Square matrix

• Rectangular matrix

Answer explanation

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.

What is the (2,3) entry of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?

• 1

• 3

• 6

• 9

Answer explanation

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 a matrix with:

• One row and multiple columns

• Multiple rows and one column

• One row and one column

• Multiple rows and multiple columns

Answer explanation

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 a matrix with:

• One row and multiple columns

• Multiple rows and one column

• One row and one column

• Multiple rows and multiple columns

Answer explanation

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 number of rows.

• They have the same number of columns.

• They have the same size and corresponding entries are equal.

• They are both square matrices.

Answer explanation

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.

If matrix A is 2x3 and matrix B is 3x4, what is the size of matrix AB?

• 2x4

• 3x3

• 4x2

• The product is undefined.

Answer explanation

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 only defined for matrices of:

• The same size

• Different sizes

• Square matrices

• Rectangular matrices

Answer explanation

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.

If A and B are m x n matrices, then A + B is:

• An m x n matrix

• An n x m matrix

• A scalar value

• Undefined

Answer explanation

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.