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# Class 12 NCERT Solutions- Mathematics Part I – Chapter 4 Determinants – Exercise 4.6 | Set 1

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

### 2x + 3y = 3

Solution:

Matrix form of the given equations is AX = B

where, A = , B = and, X = ∴ Now, |A| = ∵ Inverse of matrix exists, unique solution.

∴ System of equation is consistent.

### x + y = 4

Solution:

Matrix form of the given equations is AX = B

where, A = , B = and, X =  Now, |A| = ∵ Inverse of matrix exists, unique solution.

∴ System of equation is consistent.

### 2x + 6y = 8

Solution:

Matrix form of the given equations is AX = B

where, A = , B = and, X = ∴ Now, |A| = And, adj. A = ∴ (adj. A) B = ∵ Have no common solution.

∴ System of equation is inconsistent.

### ax + ay + 2az = 4

Solution:

Matrix form of the given equations is AX = B

where, A = , B = and, X = ∴ Now, |A| = ∵ Inverse of matrix exists, unique solution.

∴ System of equation is consistent.

### 3x – 5y = 3

Solution:

Matrix form of the given equations is AX = B

where, A = , B= and, X =  Now, |A| = And, adj. A = ∴ (adj. A) B = ∴ System of equation is inconsistent.

### 5x – 2y + 6z = –1

Solution:

Matrix form of the given equations is AX = B

where, A = , B = and, X=  Now, |A| = ∵ Inverse of matrix exists, unique solution.

∴ System of equation is consistent.

### 7x + 3y = 5

Solution:

Matrix form of the given equations is AX = B

where, A= , B= , X=  Now, |A|= ∴Unique solution

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

### 3x + 4y = 3

Solution:

Matrix form of the given equations is AX = B

where, A= , B= , X=  Now, |A|= ∴Unique solution

Now, X = A-1 (adj.A)B Therefore, x=-5/11 and y=12/11

### 3x – 5y = 7

Solution:

Matrix form of the given equations is AX = B

where, A= , B= , X=  Now, |A|= ∴Unique solutio n

Now, X =A-1 A(adj.A)B Therefore, x= -6/11 and y= -19/11

### 3x + 2y = 5

Solution:

Matrix form of the given equations is AX = B

where, A= , B= , X=  Now, |A|= ∴Unique solution

Now, X = A-1B A(adj.A)B Therefore, x= -1 and y= 4

### Chapter 4 Determinants – Exercise 4.6 | Set 2

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