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Given-matrices-A-x-x-1-3-4-x-3-M-2-R-The-smallest-det-A-x-is-

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Question Number 55374 by gunawan last updated on 23/Feb/19
Given matrices A(x)= [((x−1),3),(4,(x+3)) ]∈ M_2 (R). The smallest det(A(x)) is..
GivenmatricesA(x)=[x−134x+3]∈M2(R).Thesmallestdet(A(x))is..
Answered by Joel578 last updated on 23/Feb/19
∣A(x)∣ = (x − 1)(x + 3) − 12 = x^2 + 2x − 15 = (x + 1)^2 − 16 So the smallest ∣A(x)∣ is −16, when x = −1
∣A(x)∣=(x−1)(x+3)−12=x2+2x−15=(x+1)2−16Sothesmallest∣A(x)∣is−16,whenx=−1

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