Question

construct a 3x4 matrix whose entry aij=[2i_5j]. then the value of a12+a23+a34 is​

Answer 1

Question →

Construct a matrix of 3×4 order whose entry

aij = | 2i - 5j | . And then find the value of a12 + a23 + a34 .

Solution :-

The order of Matrix is 3×4 .

So the matrix will be :-

$\left[\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\end{array}\right]$

The Matrix is given as $a_{ij} = | 2i - 5j |$

So $a_{11} = | 2 - 5 |$

→ $a_{11} = | -3|$ = 3

$a_{12} = | 2 - 5(2) |$

→ $a_{12} = | 2 - 10 |$ = 8

$a_{13} = | 2 - 5(3) |$

→ $a_{13} = | 2 - 15 |$ = 13

$a_{14} = | 2 - 5(4) |$

→ $a_{14} = | 2 - 20|$ = 18

$a_{21} = | 2(2) - 5 |$

→ $a_{21} = | -1 |$ = 1

$a_{22} = | 2(2) - 5(2) |$

→ $a_{22} = | 4 - 10 |$ = 6

$a_{23} = | 2(2) - 5(3) |$

→ $a_{23} = | 4 - 15 |$ = 11

$a_{24} = | 2(2) - 5(4) |$

→ $a_{24} = | 4 - 20 |$ = 16

$a_{31} = | 2(3) - 5 |$

→ $a_{31} = | 6 - 5 |$ = 1

$a_{32} = | 2(3) - 5(2) |$

→ $a_{32} = | 6 - 10 |$ = 4

$a_{33} = | 2(3) - 5(3) |$

→ $a_{33} = | 6 - 15 |$ = 9

$a_{34} = | 2(3) - 5(4) |$

→ $a_{34} = | 6 - 20 |$ = 14.

From the above information we conclude that the matrix will be :-

$\left[\begin{array}{cccc}3&8&13&18\\1&6&11&16\\1&4&9&14\end{array}\right]$

Now value of $a_{12} + a_{23} + a_{34}$

a12 = 8 , a23 = 11 and a34 = 14 .

→ 8 + 11 + 14 = 33.