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प्रश्न
Find non singular matrices P & Q such that PAQ is in normal form where A `[[2,-2,3],[3,-1,2],[1,2,-1]]`
उत्तर
Matrix in PAQ form is given by ,
A=P A Q
`[[2,-2,3],[3,-1,2],[1,2,-1]]`=`[[1,0,0],[0,1,0],[0,0,1]] A[[1,0,0],[0,1,0],[0,0,1]] `
`R_1→R_3` ,
`[[1,2,-1],[3,-1,2],[2,-2,-3]] =[[1,0,0],[0,1,0],[0,0,1]] A[[1,0,0],[0,1,0],[0,0,1]] `
`R_2-3R_1,R_3-2R_1`
`[[1,2,-1],[0,-7,5],[0,-6,5]]=[[0,0,1],[0,1,-3],[1,0,-2]] A[[1,0,0],[0,1,0],[0,0,1]] `
𝑪𝟐−𝟐𝑪𝟏,𝑪𝟑+𝑪𝟏,
Now A is in normal form with rank 3.
Compare with PAQ form ,
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