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# 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.

âˆ´ |A| =

âˆ´ 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

âˆ´ |A| =

âˆ´ 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.

âˆ´ |A| =

âˆ´ 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.

âˆ´ |A| =

âˆ´ 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|=

âˆ´ |A|=

Means, A-1 exists.

Now,

From eq. (1),

A-1=

Now, Matrix form of given equation is AX = B

i.e.

âˆµ Solution is unique.

âˆ´ X=A-1B

â‡’

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|=

âˆ´ Solution is unique

Now,