Solve a2-1 ab ac ab b2-1 bc ac bc c2-1 - a2 - b2 - c2 - 1-

a ^ 2 +1 amp; ab amp; ac ab amp; b^ 2 +1 amp; bc ac amp; bc amp; a ^ 2 +1 =a^ 2 +b^ 2 +c^ 2 +1 Takes L.H.S = a ^ 2 ...

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Equation of a Line Passing through 2 Points

Solve a2+1 ...

Question

Prove that $∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 1 & a b & a c a b & b^{2} + 1 & b c a c & b c & c^{2} + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = a^{2} + b^{2} + c^{2} + 1$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 1 & a b & a c a b & b^{2} + 1 & b c a c & b c & c^{2} + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = k + a^{2} + b^{2} + c^{2}

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∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 1 & a b & a c a b & b^{2} + 1 & b c c a & c b & c^{2} + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 1 + a^{2} + b^{2} + c^{2}

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 1 & a b & a c a b & b^{2} + 1 & b c a c & b c & c^{2} + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ =

|\begin{matrix} a^{2} + 1 & a b & a c \\ a b & b^{2} + 1 & b c \\ c a & c b & c^{2} + 1 \end{matrix}| = 1 + a^{2} + b^{2} + c^{2}

⎛ ⎜ ⎝ \begin{matrix} a^{2} + 1 & a b & a c a b & b^{2} + 1 & b c c a & c b & c^{2} + 1 \end{matrix} ⎞ ⎟ ⎠ = 1 + a^{2} + b^{2} + c^{2}

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