Question

Construct a 3*3 matrix whose elements are aij = i*j

Answer 1

3*3 matrix

a11. a12. a13

a21. a22. a23

a31. a32. a33



a i j =I*j

a11 =1*1. a12=1*2. a13= 1*3

a21=2*1. a22=2*2. a23=2*3


a31=3*1. a32=3*2. a33=3*3



so,t he answer is

1. 2. 3

2. 4. 6.

3. 6. 9

Answer 2

Constructing a matrix

We have to construct a 3 × 3 matrix whose elements are of the form:

$\quad\quad\quad a_{ij}=i\times j$

We have the components of the matrix:

$\quad a_{11}=1\times 1=1$

$\quad a_{12}=1\times 2=2$

$\quad a_{13}=1\times 3=3$

$\quad a_{21}=2\times 1=2$

$\quad a_{22}=2\times 2=4$

$\quad a_{23}=2\times 3=6$

$\quad a_{31}=3\times 1=3$

$\quad a_{32}=3\times 2=6$

$\quad a_{33}=3\times 3=9$

If A be a 3 × 3 matrix, we can write:

$A=\left[\begin{array}{ccc} a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{array}\right]$

$=\left[\begin{array}{ccc} 1&2&3\\ 2&4&6\\ 3&6&9\end{array}\right]$

This is the required matrix.

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