Solution of a system of equations using matrix

Last updated at Dec. 16, 2024 by

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

 

Solution of a system of equations using matrix - Part 2

 

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

Solution of a system of equations using matrix - Part 3

 

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 

 

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo