Question

3. Construct a (2 x 3) matrix, whose elements aij are given by aij = (3i - j)​

Answer 1

Answer:

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

Step-by-step explanation:

The required matrix has 2 rows and 3 columns.

It is given by:

$\left[\begin{array}{ccc}a_1_1&a_1_2&a_1_3\\a_2_1&a_2_2&a_2_3&\end{array}\right]$

Now, according to the question it is given by:

$a_i_j = (3i - j)$

Therefore:

$a_1_1 = 3(1) - 1 = 2$

$a_1_2 = 3(1) - 2 = 1$

$a_1_3 = 3(1) - 3 = 0$

$a_2_1 = 3(2) - 1 = 5$

$a_2_2 = 3(2) - 2 = 4$

$a_2_3 = 3(2) - 3 = 3$

So, the required matrix is:

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

Answer 2

Answer:

[ 2 1 0]

[ 5 4 3]

Step-by-step explanation:

[a¹¹ a¹² a¹³

a²¹ a²² a²³]

a¹¹ = 3(1) - 1 = 2

a¹² = 3(1) - 2 = 1

a¹³ = 3(1) - 3 = 0

a²¹= 3(2) - 1 = 5

a²²= 3(2) - 2= 4

a²³ = 3(2) - 3 =3