Consider the matrices 4-17] ¹=[₁₂7], B = [1 2] ₁ A 5-7] [2] = i) Find A¹0 times vector b by writing vector bas linear combination of eigen vectors of A ii) Find a formula for AK for all non-negative integers k. (Can k be a negative integer?) iii) Use (ii) to find A¹0 times vector band compare it with what you found in (i).

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