Solution of a system of equations using matrix

Last updated at August 14, 2026 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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