Question

Easy method to find inverse of a matrice? via elementary operations[question in drawing]

Answer 1

@dan815

Answer 2

reduce it into triangular matrix and simply multiply the diagonal elements

Answer 3

http://1.bp.blogspot.com/_ue1VUbFmrsE/TEYpgdt_A8I/AAAAAAAAAEQ/JbyOjk7JN7U/s1600/Matrix_5.bmp

Answer 4

@rational lol no I would LOVE to do that but its kinda compulsory to do it via elementary operations.. those steps

I got this answer after 10 minutes.. in 9 steps

Answer 5

you are reducing it to an identity matrix ?
or looking for a general formula for inverse of nonsingular 3x3 matrices

Answer 6

A = IA
converting A to I while simultaneously doing the same operation to I to get the inverse.. that thing

Answer 7

yeah it takes 9 or so steps

Answer 8

$$

\Large \left( A| I \right) \to \left( I~| A^{-1} \right)
$$

Answer 9

Its just that.. I do a lot.. a LOT of calculation mistakes, and 9 steps in an exam will freak me out and I'll end up wasting 20% of the time on this problem yielding about 1 - 2 out of 4 marks

Answer 10

if there was some sort of step by step guide :/ follow through by making a corner 0 or something xD

Answer 11

$$


\Large {

\left( \begin{array}{ccc|ccc}
1 & 3 & -2 & 1 &0 & 0\\
-3 & 0 & -5 & 0 &1& 0 \\
2 & 5 & 0 & 0 &0 &1 \\

\end{array}
\right)
\\
R_2 +3R_1
\to
\left( \begin{array}{ccc|ccc}
1 & 3 & -2 & 1 &0 & 0\\
0 & 9 & -11 & 3 &1& 0 \\
2 & 5 & 0 & 0 &0 &1 \\

\end{array}
\right)\\




R_3+ (\hbox{-}2)\cdot R_1\to \left( \begin{array}{ccc|ccc}
1 & 3 & -2 & 1 &0 & 0\\
0 & 9 & -11 & 3 &1& 0 \\
0 & -1 & 4 & -2 &0 &1 \\

\end{array}
\right)

}
$$

Answer 12

personal preference is to use the mechanical method -- outlined very clearly on the link below. dull as ditch water but that is its strength too. if the answer doesn't look right, you're not going back through linear algebra, you're really just checking simple arithmetic, provided you've remembered the steps. v useful in an exam.

http://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html

method applied to above is attached.