Q42 of 98 Page 310

The sum of three numbers is 2. If twice the second number is added to the sum of first and third, we get 1. On adding the sum of second and third numbers to five times the first, we get 6. Find the three numbers by using matrices.


Let the three numbers be x, y and z.


According to the question,


X + y + z = 2


X + 2y + z = 1


5x + y + z = 6


Converting the following equations in matrix form,


AX = B



R2 – R1


R3 – R1



Converting back into the equations we get


X + y + z = 2


Y = - 1


4x = 5


X =


– 1 + z = 2


Z = 2 - + 1


Z =


∴ The numbers are .


More from this chapter

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40

= 10, = 10,

= 13


Ans. x = , y = , z =


41

= 4; = 0;

= 2. (x, y, z ≠ 0)


 43

The cost of 4 kg potato, 3 kg wheat and 2 kg of rice is ₹ 60. The cost of 1 kg potato, 2 kg wheat and 3 kg of rice is ₹45. The cost of 6 kg potato, 2 kg wheat and 3 kg of rice is ₹70. Find the cost of each item per kg by matrix method.

 44

An amount of ₹ 5000 is put into three investments at 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹358. If the total annual income from first two investments is ₹70more

than the income from the third, find the amount of each investment by the matrix method.


HINT: Let these investments be ₹x, ₹y and ₹z, respectively.


Then, x + y + z = 5000, …(i)


= 358


6x + 7y + 8z = 35800 …(ii)


And,


6x + 7y - 8z = 7000. …(iii)