In determinants- is the following operation allowed on a 3-3 matrix- R1 nbsp- R1 nbsp- -R2 nbsp- nbsp- R3-

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Scalar Matrix

In determinan...

Question

In determinants, is the following operation allowed on a 33 matrix?
R₁ = R₁ + (R₂ R₃)

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A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦

R_{2}

\to

R_{2}

R_{3}

R_{1}

\to

R_{1} - R_{2}

R_{3}

\to

R_{3}

R_{2}

Δ

r_{1} + r_{2} + r_{3} - r = 4 R

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = Δ^{2}

△ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

\frac{R_{1}}{r_{1}} + \frac{R_{2}}{r_{2}} + \frac{R_{3}}{r_{3}} =

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}

r_{1}, r_{2}

r_{3}

2 s

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