Using properties of determinants- prove that a2 -2a 2a-1 1 2a-1 a-2 1 3 3 1 - a-1 3

Let = a^2+2a amp;2a + 1 amp;1 2a+1 amp; a+2 amp;1 3 amp; 3 amp;1 Operating R_1 → R_1 R_2, we have = a^2 1 amp;a 1 amp;0 2a ...

You visited us 52 times! Enjoying our articles? Unlock Full Access!

Definition of a Determinant

Using propert...

Question

Using properties of determinants, prove that $∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 2 a & 2 a + 1 & 1 2 a + 1 & a + 2 & 1 3 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = {(a - 1)}^{3}$

Open in App

Solution

Suggest Corrections

Similar questions

∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 2 a & 2 a + 1 & 1 2 a + 1 & a + 2 & 1 3 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = (a - 1)^{C}

C =

∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 2 a & 2 a + 1 & 1 2 a + 1 & a + 2 & 1 3 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = {(a - 1)}^{2}

|\begin{matrix} 1 + a & 1 & 1 \\ 1 & 1 + a & 1 \\ 1 & 1 & 1 + a \end{matrix}| = a^{3} + 3 a^{2}

|\begin{matrix} a^{2} + 2 a & 2 a + 1 & 1 \\ 2 a + 1 & a + 2 & 1 \\ 3 & 3 & 1 \end{matrix}| = {(a - 1)}^{3}

∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 2 a & 2 a + 1 & 1 2 a + 1 & a + 2 & 1 3 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = {(a - 1)}^{3}

∣ ∣ ∣ ∣ ∣ \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}

Join BYJU'S Learning Program