Square Matrix

Q.

Matrix $A=[a_{ij}{]}_{m\times n}$ is a square matrix if _______

1. m > n

2. m = 1

3. m = n

4. m < n

Q.

A square matrix is having p number of rows. What is ‘j’ if $a_{ij}$ is situated in the last row and second last column

1. 2

2. p + 2

3. p - 1

4. 2p

Q. Which of the following is not a type of matrix?

1. Rectangular matrix
2. Square matrix
3. Null matrix
4. Circular matrix

Q. The relation between number of rows(r) and number of columns(c) of a square matrix is :

1. r > c
2. r < c
3. r = 2c
4. r = c

Q.

Matrix $A=\left[\begin{array}{cccc}2& 0& 1& 1\\ 0& -1& -2& 3\\ 0& 0& 1& 4\\ 0& 0& 0& 2\end{array}\right]$ is a ___ matrix

1. Unit Matrix

2. Rectangular Matrix

3. Upper triangular matrix

4. Lower triangular matrix

Q. Given,
$2\left[\begin{array}{cc}5& 3\\ 4& 2\end{array}\right]=\left[\begin{array}{cc}10& 6\\ 8& m\end{array}\right]$
What is the value of m?

1. 3
2. 1
3. 8
4. 4

Q.

A square matrix is having p number of rows. What is ‘j’ if $a_{ij}$ is situated in the last row and second last column

1. p + 2

2. p - 1

3. 2p

4. 2

Q. Given,
$\left[\begin{array}{cc}2& 4\\ 3& 5\end{array}\right]+\left[\begin{array}{cc}4& 3\\ 2& 1\end{array}\right]=\left[\begin{array}{cc}6& 7\\ x& 6\end{array}\right]$
What is the value of x?

1. 6
2. 5
3. 8
4. 7

Q.

$MatrixA=\left(\begin{array}{ccccc}1& 1& 1& 1& 1\\ 1& 2& 3& 4& 5\\ 1& 3& 6& 10& 15\\ 1& 4& 10& 20& 35\\ 1& 5& 15& 35& 70\end{array}\right)$ is a ___ matrix of order ___

1. Square, $4\times 4$

2. Rectangular, $5\times 5$

3. Rectangular $4\times 5$

4. Square , $5\times 5$

Q.

Given $A=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right];B=\left[\begin{array}{cc}4& 2\\ 1& 0\end{array}\right];C=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

Find A(B+C)

1. $\left[\begin{array}{cc}17& 16\\ 26& 24\end{array}\right]$

2. $\left[\begin{array}{cc}7& 6\\ 6& 4\end{array}\right]$

3. $\left[\begin{array}{cc}17& 6\\ 26& 4\end{array}\right]$

4. $\left[\begin{array}{cc}7& 16\\ 6& 24\end{array}\right]$

Q.

Identify the square matrix in the following-

1. $\left[\begin{array}{ccc}2& 1& 3\\ 4& 1& 7\end{array}\right]$

2. $\left[\begin{array}{cc}-5& 2\\ -1& 3\\ 4& -4\end{array}\right]$

3. $\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]$

4. $\left[\begin{array}{c}2\\ 1\\ -2\end{array}\right]$

Q. Prove that 2-\surd3 is an irrationa

Q. The transpose of a rectangular matrix is a

1. diagonal matrix
2. scalar matrix
3. square matrix
4. rectangular matrix

Q. Let M be a $2\times 2$ symmetric matrix with integer entries. Then, M is invertible if

1. the first column of M is the transpose of the second row of M
2. the second row of M is the transpose of the first column of M
3. M is a diagonal matrix with non-zero entries in the main diagonal
4. the product of entries in the main diagonal of M is not the square of an integer