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If A = [(2,1)(-4,-2)], then the value of I + 2A + 3A^2 + --------- ∞ is

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If A = [(2,1)(-4,-2)],  then the value of I + 2A + 3A2 + --------- ∞ is

(a)   [(4,1)(-4,0)]

(b)   [(3,1)(-4,-1)]

(c)   [(5,2),(-8, -3)]

(d)   none of these

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Best answer

Correct option  (c)   [(5,2),(-8, -3)]

Explanation:

I + 2A + 3A2 + 4A3 ........ ∞

= I + 2A (∴ A2 = 0, A3 = A4 = ...... = 0)

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