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

• Difficulty Level : Expert
• Last Updated : 12 Oct, 2021

2x + 3y = 3

Solution:

Matrix form of the given equations is AX = B

where, A = , B =   and, X =

âˆ´

Now, |A| =

âˆµ Inverse of matrix exists, unique solution.

âˆ´ System of equation is consistent.

x + y = 4

Solution:

Matrix form of the given equations is AX = B

where, A =, B =  and, X =

âˆ´

Now, |A| =

âˆµ Inverse of matrix exists, unique solution.

âˆ´ System of equation is consistent.

2x + 6y = 8

Solution:

Matrix form of the given equations is AX = B

where, A =, B =  and, X =

âˆ´

Now, |A| =

And, adj. A =

âˆ´ (adj. A) B =

âˆµ Have no common solution.

âˆ´ System of equation is inconsistent.

ax + ay + 2az = 4

Solution:

Matrix form of the given equations is AX = B

where, A =, B =and, X =

âˆ´

Now, |A| =

âˆµ Inverse of matrix exists, unique solution.

âˆ´ System of equation is consistent.

3x – 5y = 3

Solution:

Matrix form of the given equations is AX = B

where, A =, B=and, X =

âˆ´

Now, |A| =

And, adj. A =

âˆ´ (adj. A) B =

âˆ´ System of equation is inconsistent.

5x – 2y + 6z = â€“1

Solution:

Matrix form of the given equations is AX = B

where, A =, B = and, X=

âˆ´

Now, |A| =

âˆµ Inverse of matrix exists, unique solution.

âˆ´ System of equation is consistent.

7x + 3y = 5

Solution:

Matrix form of the given equations is AX = B

where, A=, B=, X=

âˆ´

Now, |A|=

âˆ´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=

âˆ´

Now, |A|=

âˆ´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=

âˆ´

Now, |A|=

âˆ´Unique solutionn

Now, X =A-1A(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=

âˆ´

Now, |A|=

âˆ´Unique solution

Now, X = A-1BA(adj.A)B

Therefore, x= -1 and y= 4

Chapter 4 Determinants – Exercise 4.6 | Set 2

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