Question

if a=(1,0,0),(2,1,0),(3,3,1) then reduce it to I3 by using column transformation
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Answer 1

Given:

$a= \left[\begin{array}{ccc}1&0&0\\2&1&0\\3&3&1\end{array}\right]$

To find:

$I_3=?$

Solution:

$a= \left[\begin{array}{ccc}1&0&0\\2&1&0\\3&3&1\end{array}\right]$

calculate |a|:

$\bold{|a|= [1(1-0) -0(2-0)+0(6-3)]}$

    $=[1(1)-0(2)+0(3)]\\\\=[1-0+0]\\\\= 1$

where a is not a singular matrix.

Calculating $a^{-1} :$

$\to C_1= C_1- 2C_2$

$a= \left[\begin{array}{ccc}1&0&0\\0&1&0\\-3&3&1\end{array}\right]$

$\to C_1= C_1+3C_3\\\\a= \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&3&1\end{array}\right]\\\\\to C_2= C_2+3C_3\\\\a= \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

$I_3= a$