2. Example-2
1. is Strictly 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 Strictly Diagonally Dominant
2. is Strictly Diagonally Dominant Matrix ?
`[[9,8,7],[6,5,4],[3,2,1]]`
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=[[9,8,7],[6,5,4],[3,2,1]]`
`Row 1:|a_(11)|=|9|=9,+|a_(12)|+|a_(13)|=+|8|+|7|=15`
`9 > 15?` no
`Row 2:|a_(22)|=|5|=5,+|a_(21)|+|a_(23)|=+|6|+|4|=10`
`5 > 10?` no
`Row 3:|a_(33)|=|1|=1,+|a_(31)|+|a_(32)|=+|3|+|2|=5`
`1 > 5?` no
So, given matrix is not Strictly Diagonally Dominant
This material is intended as a summary. Use your textbook for detail explanation.
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