Show that x - 4 2x 2x 2x x - 4 2x 2x 2x x - 4 - 5x - 4 4 - x2

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Properties of Determinants

Show that x...

Question

Show that $∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = (5 x + 4) (4 - x)^{2}$

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∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = (5 x + 4) (4 - x)^{2}

det ∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣

= (5 x + 4) (4 - x)^{2}

∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = (5 x + 4) (4 - {x)}^{2}

∣ ∣ ∣ ∣ \begin{matrix} y + k & y & y y & y + k & y y & y & y + k \end{matrix} ∣ ∣ ∣ ∣ = k^{2} (3 y + k)

∣ ∣ ∣ ∣ \begin{matrix} x - 4 & 2 x & 2 x 2 x & x - 4 & 2 x 2 x & 2 x & x - 4 \end{matrix} ∣ ∣ ∣ ∣ = (A + B x) (x - A)^{2}

(A, B)

∣ ∣ ∣ ∣ \begin{matrix} x - 4 & 2 x & 2 x 2 x & x - 4 & 2 x 2 x & 2 x & x - 4 \end{matrix} ∣ ∣ ∣ ∣ = (A + B x) {(x - A)}^{2}

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