2. Example-2
1. is Diagonally Dominant Matrix ?
`[[3,1,2],[2,4,1],[1,1,2]]`
Solution:
A Square matrix `A` is called diagonally dominant matrix, if `A_(ii)>=sum_(i!=j)^()|A_(ij)|`
and `A` is called strictly diagonally dominant matrix, if `A_(ii)>sum_(i!=j)^()|A_(ij)|`
`A=[[3,1,2],[2,4,1],[1,1,2]]`
`Row 1:|a_(11)|=|3|=3,+|a_(12)|+|a_(13)|=+|1|+|2|=3`
`3 >= 3?` yes
`Row 2:|a_(22)|=|4|=4,+|a_(21)|+|a_(23)|=+|2|+|1|=3`
`4 >= 3?` yes
`Row 3:|a_(33)|=|2|=2,+|a_(31)|+|a_(32)|=+|1|+|1|=2`
`2 >= 2?` yes
So, given matrix is Diagonally Dominant
2. is Diagonally Dominant Matrix ?
`[[5,1,2],[3,8,4],[0,2,3]]`
Solution:
A Square matrix `A` is called diagonally dominant matrix, if `A_(ii)>=sum_(i!=j)^()|A_(ij)|`
and `A` is called strictly diagonally dominant matrix, if `A_(ii)>sum_(i!=j)^()|A_(ij)|`
`A=[[5,1,2],[3,8,4],[0,2,3]]`
`Row 1:|a_(11)|=|5|=5,+|a_(12)|+|a_(13)|=+|1|+|2|=3`
`5 >= 3?` yes
`Row 2:|a_(22)|=|8|=8,+|a_(21)|+|a_(23)|=+|3|+|4|=7`
`8 >= 7?` yes
`Row 3:|a_(33)|=|3|=3,+|a_(31)|+|a_(32)|=+|0|+|2|=2`
`3 >= 2?` yes
So, given matrix is Diagonally Dominant
This material is intended as a summary. Use your textbook for detail explanation.
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