Suppose we have to solve

a 1 x + b 1 x + c 1 x = d 1

a 2 x + b 2 x + c 2 x = d 2

a 3 x + b 3 x + c 3 x = d 3

We use matrices to solve this

We write the equation as

Solution of a system of equations using matrix - teachoo.jpg

We need to find x, y, z

i.e.

We need to find matrix X

 

1.jpg

 

But, What if |A| = 0?

If |A| = 0

Then, we calculate (adj A) B

  • If (adj A) B ≠ O,
    Solution does not exist,
    And system of equation is inconsistent

  • If (adj A) B = O,
    Equation may have infinite solution, or no solution

To summarize

37.jpg

 

Solve equations

 2x + 5y = 1

 3x + 2y = 7

Veiw solution – Example 27

 

Solve equations

  3x – 2y + 3z = 8

  2x + y – z = 1

  4x – 3y + 2z = 4

 

View solution – Example 28 

 

  1. Chapter 4 Class 12 Determinants
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.