1 markMCQSection A

Which of the following cannot be the order of a row-matrix?

Q: Which of the following cannot be the order of a row-matrix?

**Correct option: (A) $2 \times 1$** A row matrix has exactly 1 row, so its order must always be of the form $1 \times n$. An order of $2 \times 1$ describes a matrix with 2 rows and 1 column, which is a column matrix, not a row matrix.

Q: What is the difference between a row matrix and a column matrix?

A row matrix has exactly one row and order $1 \times n$, while a column matrix has exactly one column and order $m \times 1$. They represent different arrangements of the same number of elements.

Matrices

Order of a Row Matrix

Options

(A)

2 \times 1

(B)

1 \times 2

(C)

1 \times 1

(D)

1 \times n

Official Answer

Correct option: (A) $2 \times 1$

A row matrix has exactly 1 row, so its order must always be of the form $1 \times n$ . An order of $2 \times 1$ describes a matrix with 2 rows and 1 column, which is a column matrix, not a row matrix.

row matrixcolumn matrixorder of matrix1 x nmatrix definitionsrows and columns

Marking Scheme

11 mark: correct option (A) selected.

Hint

A row matrix must have exactly one row — its order is always written as $1 \times n$ , never $m \times 1$ .

Quick Oral Answer

A row matrix always has exactly one row, so its order is $1 \times n$ ; $2 \times 1$ has two rows, making it a column matrix instead, so the answer is (A).

Analysis & Explanation

This checks the basic definition of a row matrix versus a column matrix.

Concept

A row matrix is defined as a matrix having exactly one row, so its order is always $1 \times n$ for some positive integer n.
A column matrix has exactly one column, with order $m \times 1$ .

Why (A) is correct

$2 \times 1$ means 2 rows and 1 column — this describes a column matrix, so it can never be the order of a row matrix.

Why the other options are wrong

(B) $1 \times 2$ has 1 row and 2 columns — a valid row matrix.
(C) $1 \times 1$ has 1 row and 1 column — technically satisfies the $1 \times n$ form with n = 1, so it is a valid (trivial) row matrix.
(D) $1 \times n$ is exactly the general form of a row matrix's order, so it is always valid.

Common Mistakes

1Confusing row matrix ( $1 \times n$ ) with column matrix ( $m \times 1$ ) and picking (D) by mistake.
2Assuming a $1\times1$ matrix cannot be a row matrix, when in fact it satisfies both row and column matrix definitions simultaneously.

Interesting Facts

A $1\times1$ matrix is the only type of matrix that is simultaneously a row matrix, a column matrix, a square matrix, a diagonal matrix, and a scalar matrix.

Row and column matrices are the building blocks of vectors in linear algebra — a row matrix represents a row vector, commonly used in coordinate geometry and computer graphics transformations.

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Frequently Asked Questions

What is the difference between a row matrix and a column matrix?

A row matrix has exactly one row and order $1 \times n$ , while a column matrix has exactly one column and order $m \times 1$ . They represent different arrangements of the same number of elements.

Can a matrix be both a row matrix and a column matrix?

Yes, only a $1\times1$ matrix satisfies both definitions simultaneously, since it has exactly one row and exactly one column.