Let P=[(3,-1,-2),(2,0,alpha),(3,-5,0)] ,...

Let `P=[(3,-1,-2),(2,0,alpha),(3,-5,0)]` , where ` alpha in R ` . Suppose ` Q =[q_(ij)]` is a matrix satisfying `PQ = KI_3` for some non - zero `K in R .` If ` q_(23) =- (K)/(8) and |Q| = (k^2)/(2),` then `alpha^2 + k^2 ` is equal to ________.

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Let P=[(3,-1,-2),(2,0,alpha),(3,-5,0)] , where alpha in R . Suppose Q =[q_(ij)] is a matrix satisfying PQ = KI_3 for some non - zero K in R . If q_(23) =- (K)/(8) and |Q| = (1)/(2), then alpha^2 + k^2 is equal to ________.

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Let `P=[(3,-1,-2),(2,0,alpha),(3,-5,0)]` , where ` alpha in R ` . Suppose ` Q =[q_(ij)]` is a matrix satisfying `PQ = KI_3` for some non - zero `K in R .` If ` q_(23) =- (K)/(8) and |Q| = (k^2)/(2),` then `alpha^2 + k^2 ` is equal to ________.

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