Question

An amount of rs. 8000 is distributed into three investments at the rate of 7%,8% and 9% per annum respectively is rs. 5 more than the second. Find the amount of each investment using matrix algebra ?
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Answer 1

❍ Let investments be x, y, z.

x=100

6×5000=300

y= 100

7×5000=350z= 100

8×5000 =400

❍ Now,

6x+7y+8z=100

x+y+z=358

x+y−z=70

Δx=B

611

711 81−1

xyz = 100 358

70 =Δ= 611

711 81−1

❍ Step by step explanation :

=(−6+8+7)−(8+6−7)

=9−7=2 Δ 1

= 100 358

70 711 81−1

=(−100+358×8+490)−(560+100−7×358)

=−70+15×358

=5300 Δ 2

= 611

100 358 70 81−1

=(−6×358+100−560)−(8×358+420−100)

=−14×358+660−320

=−4672

Δ 3= 611 711 100 358 70

=(1420+100+7×358)−(100+6×358+490)

=288 x= Δ Δ 1

= 25300

=2650 y= Δ

Δ 2= 2−4672 =2336z= Δ

Δ 3 = 2288 =144

Amount of each investment is Rs. 2650, Rs. 2336, Rs. 144.

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