# Find k if the following matrix is singular: [k-1233121-24] - Mathematics and Statistics

Sum

Find k if the following matrix is singular:

[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]

#### Solution

Let C = [("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]

Since C is a singular matrix, ICI = 0

∴ |("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)| = 0

∴ (k – 1)(4 + 4) – 2(12 – 2) + 3( – 6 – 1) = 0

∴ 8k – 8 – 20 – 21 = 0

∴ 8k = 49

∴ k = 49/8

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Determinants and Matrices
Exercise 4.4 | Q 4. (iii) | Page 83