Elements of a Matrix

Q.

State whether True or False - If $\left[a_{ij}\right]$ is an element of matrix A then it lies in $i^{th}$ row and $j^{th}$ column of the matrix.

1. True

2. False

Q.

If A = $(a_{ij}{)}_{2\times 2}$ , where $a_{ij}$ = i + j, then A is equal to

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

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

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

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

Q.

If $\left[a_{ij}\right]$ is an element of matrix A then it lies in $i^{th}$ row and $j^{th}$ column of the matrix.

1. True

2. False

Q. Construct the matrix of order $3\times 2$ whose elements are given by $a_{ij}=2i-j$

1. $\left[\begin{array}{cc}1& 3\\ 0& 2\\ -1& 1\end{array}\right]$
2. $\left[\begin{array}{ccc}1& 3& 5\\ 0& 2& 4\end{array}\right]$
3. $\left[\begin{array}{cc}1& 0\\ 3& 2\\ 5& 4\end{array}\right]$
4. $\left[\begin{array}{ccc}1& 0& -1\\ 3& 2& 1\end{array}\right]$

Q. Matrix A has 12 elements. Which of the following cannot be the possible number of rows and columns of matrix A?​

1. Matrix A has 6 rows and 2 columns​
2. Matrix A has 1 row and 12 columns​
3. Matrix A has 3 rows and 4 columns​
4. Matrix A has 7 rows and 1 column​

Q.

Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i<j$ and $a_{ij}=i+j$ if $i\ge j$.

1. $\left(\begin{array}{ccc}4& 5& 6\\ 0& 3& 4\\ 0& 0& 2\end{array}\right)$

2. $\left(\begin{array}{ccc}4& 5& 6\\ 3& 4& 0\\ 2& 0& 0\end{array}\right)$

3. $\left(\begin{array}{ccc}2& 0& 0\\ 3& 4& 0\\ 4& 5& 6\end{array}\right)$

4. $\left(\begin{array}{ccc}0& 0& 0\\ 1& 2& 3\\ 4& 5& 0\end{array}\right)$