Maths · Determinants and matrices of order two and three

If then is equal to

If \( D_{P}=\left|\begin{array}{ccc}\boldsymbol{P} & \mathbf{1 5} & \mathbf{8} \\ \boldsymbol{P}^{2} & \mathbf{3 5} & \mathbf{9} \\ \boldsymbol{P}^{3} & \mathbf{2 5} & \mathbf{1 0}\end{array}\right|, \) then \( \boldsymbol{D}_{1}+ \) \( D_{2}+D_{3}+D_{4}+D_{5} \) is equal to

  • A. -29000
  • B. -25000
  • C. 25000
  • D. none of these

Step-by-step solution

Compute determinant as function of P: D(P) = -145P³ + 50P² + 125P. Evaluate at P=1 to 5: D(1)=30, D(2)=-710, D(3)=-3090, D(4)=-7980, D(5)=-16250. Sum = -28000, which is not among options A, B, C.
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