Question

Probten urse The llowissysk strde domingnt sustem plain onttel rearrange

Answer 1

a) A strictly diagonally dominant matrix has should follow below three conditions:

Row 1: |a11| > |a12|+|a13|

Row 2: |a22| > |a21| + |a23|

Row 3: |a33| > |a31| + a|32|

So rearranging the equations:

3u-v +w= -2 -------------------------(1)

u-8v-2w= 1---------------------------(2)

u+v+5w=4 ----------------------------(3)

The above equations form the strictly diagonal dominant system

From Equation (1) , |a11|=3, |a12|=1 and a13=1 Hence |a11| > |a12|+|a13|

From Equation (2), |a21| =1 , |a22| = 8 and |a23| = 2 Hence |a22| > |a21| + |a23|

From Equation (3) , |a31| =1 , |a32| = 1 and |a33| = 8 Hence |a33| > |a31| + |a32|

b) Refer to the below image for solution :

4A 丿瓦-丐 78