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प्रश्न
if A = `[(3, -2),(4,-2)] and l = Matric [(1,0),(0,1)]` find k so that `A^2 = kA - 2I`
उत्तर
Given: A = `[(3, -2), (4,-2)],` I = `[(1,0),(0,1)]`
`"A"^2 = "A". "A" = [(3, -2),(4,-2)] [(3, -2),(4,-2)]`
`= [(9 - 8, -6 + 4),(12 - 8, -8 + 4)]`
`= [(1,-2),(4,-4)]`
KA - 2I = K `[(3, -2),(4,-2)] - 2 [(1,0),(0,1)]`
`= [(3"k", - 2"k"),(4"k", -2"k")] - [(2, 0),(0,2)]`
`= [(3"k" + 2, -2"k"),(4"k", -2"k" + 2)]`
`"A"^2 = "KA" - 2"I"`
`[(1,-2),(4,-4)] = [(3"k" - 2, -2"k"),(4"k", -2"k" - 2)]`
3k - 2 = 1
⇒ 3k = 3
k = 1
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