Exercise 3.1.5

Answers

Multiply A − UV T with formula (9), we have

(A − UV T)M−1 = (A − UV T) (A−1 + A−1U(I − V TA−1U)−1V TA−1) = (A − UV T)A−1 + (A − UV T)A−1U(I − V TA−1U)−1V TA−1 = (A − UV T)A−1 + (I − UV TA−1)U(I − V TA−1U)−1V TA−1 = (A − UV T)A−1 + U(I − V TA−1U)(I − V TA−1U)−1V TA−1 = (A − UV T)A−1 + UV TA−1 = I − UV TA−1 + UV TA−1 = I

Where we have used the fourth identity on page 163.

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2020-03-20 00:00
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