Question

Solve the following :

If A = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`, the reduce it to unit matrix by using row transformations.

Answer 1

AB = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`

∴ |A| = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`

= 1(1 – 0) –0(2 –0) + 0(6 – 3)
= 1 – 0 + 0
= 1 ≠ 0
∴ A is non-singular matrix.
Hence, row transformations are possible.

Now, A = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`

Applying R₂ → R₂ – 2R₁ and R₃ → R₃ – 3R₁, we get

A = `[(1, 0, 0),(0, 1, 0),(0, 3, 1)]`

Applying R₃ → R₃ – 3R₂, we get

A = `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`.