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