Find inverse of the following matrices (if they exist) by elementary transformations : [2174] - Mathematics and Statistics

Sum

Find inverse of the following matrices (if they exist) by elementary transformations :

`[(2, 1),(7, 4)]`

Let A = `[(2, 1),(7, 4)]`

∴ |A| = `|(2, 1),(7, 4)|`

= 8 – 7
= 1 ≠ 0
∴ A^–1 exists.
Consider AA^–1= I

∴ `[(2, 1),(7, 4)] "A"^-1 = [(1, 0),(0, 1)]`

Applying R₁ → 4R₁ – R₂, we get

`[(1, 0),(7, 4)] "A"^-1 = [(4, -1),(0, 1)]`

Applying R₂ → R₂ – 7R₁, we get

`[(1, 0),(0, 1)] "A"^-1 = [(4, -1),(-7, 2)]`

Applying R₂ → `(1/4)` R₂, we get

`[(1, 0),(0, 1)] "A"^-1 = [(4, -1),(-7, 2)]`

∴ A^–1 = `[(4, -1),(-7, 2)]`.

Concept: Inverse of Matrix

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Chapter 2 Matrices
Miscellaneous Exercise 2 | Q 4.16 | Page 85