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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)]`

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Solution

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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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 2 Matrices
Miscellaneous Exercise 2 | Q 4.16 | Page 85
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