Class 12 NCERT Solutions – Mathematics Part I – Chapter 4 Determinants – Exercise 4.6 | Set 2

• Difficulty Level : Expert
• Last Updated : 05 Apr, 2021

3y – 5z = 9

Solution:

Matrix form of the given equation is AX = B

i.e. ∴ |A| = ∴ Solution is unique.

Now, X = A-1B = (adj.A)B Therefore, x=1, y=1/2, z=3/2

x + y + z = 2

Solution:

Matrix form of the given equation is AX = B

i.e ∴ |A| = ∴ Solution is unique.

Now, X = A-1B = (adj.A)B Therefore, x = 2, y = -1, z = 1

3x – y – 2z = 3

Solution:

Matrix form of given equation is AX = B

i.e. ∴ |A| = ∴ Solution is unique.

Now, X = A-1B = (adj.A)B Therefore, x = 1, y = 2, z = -1

2x – y + 3z = 12

Solution:

Matrix form of given equation is AX = B

i.e. ∴ |A| = ∴ Solution is unique.

Now, X = A-1B = (adj.A)B Therefore, x = 2, y = 1, z = 3

x + y – 2z = – 3

Solution:

Given: A= Now, |A|= ∴ |A|= Means, A-1 exists.

And A-1 = (adj.A)……(1)

Now, ∴ adj. A = From eq. (1),

A-1= Now, Matrix form of given equation is AX = B

i.e. ∵ Solution is unique.

∴ X=A-1B Therefore, x = 1, y = 2, z = 3

Question 16. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is 60 rupees. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is 90 rupees. The cost of 6 kg onion 2 kg wheat and 3 kg rice is 70 rupees. Find cost of each item per kg by matrix method.

Solution:

Let Rs x, Rs y, Rs z per kg be the prices of onion, wheat and rice respectively.

A.T.Q.

4x+3y+2z=60

2x+4y+6z=90

6x+2y+3z=70

Matrix form of equation is AX = B

where, A= ,B= and X= => Now, |A|= ∴ Solution is unique

Now, X=A-1B= (adj. A)B……(1)

Now, ∴ (adj.A)= From eqn.(1) Therefore, x = 5, y = 8, z = 8

Hence, the cost of onion, wheat and rice are Rs. 5, Rs 8 and Rs 8 per kg.

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