Let and . Which relation between and is always…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let Δ1=det⁡(x1y11x2y21x3y31)\Delta_1=\det\begin{pmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{pmatrix} and Δ2=det⁡(x1y11x3y31x2y21)\Delta_2=\det\begin{pmatrix}x_1&y_1&1\\x_3&y_3&1\\x_2&y_2&1\end{pmatrix}. Which relation between Δ1\Delta_1 and Δ2\Delta_2 is always true? (a) Δ2=0\Delta_2=0 (b) Δ2=−Δ1\Delta_2=-\Delta_1 (c) Δ2=Δ1\Delta_2=\Delta_1 (d) Δ2=2Δ1\Delta_2=2\Delta_1

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