From the following matrices, the one which is not a square matrix, is : (a) [5] (b) 0 1 \1 0 (c) 16 17 18 \15

Question 34 of 37

Q. From the following matrices, the one which is not a square matrix, is :

(a)

[5]

(b)

\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}

(c)

\begin{bmatrix} 16 & 17 & 18 \\ 15 & 14 & 13 \\ 12 & 11 & 10 \end{bmatrix}

(d)

\begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \end{bmatrix}

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A square matrix has equal rows and columns; option (d) is $3\times4$ , so it is not square.

The order of a matrix is written as $(\text{rows}) \times (\text{columns})$ . A matrix is square only if rows $=$ columns.

(a) $[5]$ has order $1\times 1$ — square.
(b) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ has order $2\times 2$ — square.
(c) $\begin{bmatrix} 16 & 17 & 18 \\ 15 & 14 & 13 \\ 12 & 11 & 10 \end{bmatrix}$ has order $3\times 3$ — square. …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL1 markMCQ
$Q. From the following matrices, the one which is not a square matrix, is :$
(a) $[5]$
(b) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$
(c) $\begin{bmatrix} 16 & 17 & 18 \\ 15 & 14 & 13 \\ 12 & 11 & 10 \end{bmatrix}$
(d) $\begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \end{bmatrix}$
›Reveal solutionSolution
A square matrix has equal rows and columns; option (d) is $3\times4$ , so it is not square.

The order of a matrix is written as $(\text{rows}) \times (\text{columns})$ . A matrix is square only if rows $=$ columns.

(a) $[5]$ has order $1\times 1$ — square.

(b) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ has order $2\times 2$ — square.

(c) $\begin{bmatrix} 16 & 17 & 18 \\ 15 & 14 & 13 \\ 12 & 11 & 10 \end{bmatrix}$ has order $3\times 3$ — square. …
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CBSE 2023Set ANNUAL1 mark
$Q. Express each of the following in one word / term : A matrix that consists of one element only$
›Reveal solutionSolution

A matrix having only one element is a singleton matrix (order $1\times 1$ ).

Matrices are named by their structure: a matrix with one row is a row matrix, with one column a column matrix, and a matrix that consists of only one element is of order $1\times 1$ and is called a ** …

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CBSE 2022Set ANNUAL1 markMCQ
$Q. From the following the one which is an identity matrix, is :$
(a) $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$
(b) $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}$
(c) $\begin{pmatrix} 1 & 0 \\ 0 & 0 \\ 0 & 1 \end{pmatrix}$
(d) $\begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}$
›Reveal solutionSolution

Square, diagonal $=1$ , off-diagonal $=0$ ⇒ option (a).

An identity matrix $I$ is a square matrix in which

$a_{ij}=\begin{cases}1,& i=j\\0,& i\neq j.\end{cases}$

…

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CBSE 2022Set ANNUAL1 markMCQ
$(1\ \ 2\ \ 3\ \ 4)$
(a) Square matrix
(b) Row matrix
(c) Column matrix
(d) Zero matrix
›Reveal solutionSolution

Order $1\times 4$ (a single row) ⇒ row matrix.

A matrix having only one row is called a row matrix. The given array

$(1\ \ 2\ \ 3\ \ 4)$ …

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CBSE 2022Set ANNUAL1 markMCQ
$A = [a_{ij}]$
(a) $a_{ij} = \begin{cases} 0, & \text{if } i = j \\ 1, & \text{if } i \neq j \end{cases}$
(b) $a_{ij} = \begin{cases} 1, & \text{if } i = j \\ 1, & \text{if } i \neq j \end{cases}$
(c) $a_{ij} = \begin{cases} 1, & \text{if } i = j \\ 0, & \text{if } i \neq j \end{cases}$
(d) $a_{ij} = \begin{cases} 0, & \text{if } i = j \\ 0, & \text{if } i \neq j \end{cases}$
›Reveal solutionSolution

Diagonal entries $1$ , off-diagonal entries $0$ ⇒ option (c).

The unit (identity) matrix is the square matrix with every principal-diagonal element equal to $1$ and all remaining elements equal to $0$ :

$a_{ij}=\begin{cases}1,& i=j\\0,& i\neq j.\end{cases}$

…

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CBSE 2019Set ANNUAL1 mark
$Q. Express each of the following in one word/term each:$
(iv) A type of matrix whose number of rows and number of columns are equal.
›Reveal solutionSolution

The one-word term is Square matrix.

A matrix of order $m \times n$ has $m$ rows and $n$ columns. When $m = n$ (rows = columns), it is called a square matrix, e.g. a $2 \times 2$ or $3 \times 3$ matrix such as $\begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}$ . Only square matrices have a determinant and (when …

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CBSE 2019Set ANNUAL1 markMCQ
$\begin{pmatrix} x-y & z \\ 2x-y & w \end{pmatrix} = \begin{pmatrix} -1 & 4 \\ 0 & 5 \end{pmatrix}$
(a) $1, 2, 3, 4$
(b) $1, 2, 4, 5$
(c) $1, 2, 3, 5$
(d) $1, 1, 4, 5$
›Reveal solutionSolution

Correct option: (b) $x=1,\,y=2,\,z=4,\,w=5$ .

Two matrices are equal iff their corresponding elements are equal. Comparing

$\begin{pmatrix} x-y & z \\ 2x-y & w \end{pmatrix} = \begin{pmatrix} -1 & 4 \\ 0 & 5 \end{pmatrix}$

gives four equations:

$x - y = -1, \quad z = 4, \quad 2x - y = 0, \quad w = 5.$

From $2x - y = 0$ we get $y = 2x$ . Substitute into $x - y = -1$ : …

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Q.From the following matrices, the one which is not a square matrix, is :

Concept understanding — Order and Types of Matrices

Q.From the following matrices, the one which is not a square matrix, is :

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