ISC (Commerce) Class 12CISCE
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# Find the Value of K If M = [(1,2),(2,3)] and M^2 - Km - I_2 = 0 - ISC (Commerce) Class 12 - Mathematics

#### Question

Find the value of k if M  = [(1,2),(2,3)] and M^2 - km - I_2 = 0

#### Solution

M^2 = [(1,2),(2,3)][(1,2),(2,3)] = [(1+4, 2+6),(2+6,4+9)]

M^2 = [(5,8),(8,13)]

kM = [(k,2k),(2k, 3k)]

:. M^2 - kM - I_2 =0

[(5,8),(8,13)] - [(k, 2k),(2k , 3k)] - [(1,0),(0,1)] = [(0,0),(0,0)]

[(4-k,8 - 2k),(8-2k, 12-3k)] = [(0,0),(0,0)]

4 - k = 0

k = 4

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#### APPEARS IN

2014-2015 (March) (with solutions)
Question 1.1 | 3.00 marks
Solution Find the Value of K If M = [(1,2),(2,3)] and M^2 - Km - I_2 = 0 Concept: Order of a Matrix.
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