Solution of a system of equations using matrix

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

We need to find x, y, z

i.e.

We need to find matrix X

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

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