(a) For the matrix find A = [-1 3 2 -4] find i. the matrix 1-norm ii. the matrix
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Question
(a) For the matrix find A = [-1 3 2 -4] find i. the matrix 1-norm ii. the matrix infinity-norm iii. the Frobenius norm iv. the condition number, Use the matrix 1-norm for this. (b) For the matrix B = [1 2 2 4] find i. the matrix 1-norm ii. the matrix infinity norm iii. the Frobenius norm iv. the condition number. Use the matrix 1-norm for this (c) For the matrix C = [5 0 0 0 10 0 0 0 20] find i. the matrix 1-norm ii. the matrix infinity-norm iii. the Frobenius norm. iv the condition number. Use the matrix 1-norm for this.Explanation / Answer
1. a.)
(i)
A = -1 2
3 -4
The absolute column sums of A are |-1| + 3 = 4 and 2 + | 4| = 6. The larger of these
is 6 and therefore A1 = 6.
(ii)
The absolute row sums of A are |-1 |+ 2 = 3 and 3 + | 4| = 7. The larger of these is 7
and therefore A = 7.
(iii)
the frobinius norm is
underoot (|-1|2 + |2|2 + |3|2 + |-4|2 ) = underoot(30) = 5.47
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b.) matrix B = 1 2
2 4
(i) The absolute column sums of B are 1 + 2 = 3 and 2 + 4 = 6. The larger of these
is 6 and therefore B1 = 6.
(ii) The absolute row sums of B are 1 + 2 = 3 and 2+ 4 = 6. The larger of these is 6
and therefore B = 6
(iii) the frobinius norm is
underoot( |1|2 + |2|2 + |2|2 + |4|2 )=underoot(25) = 5
c.)
matrix C = 5 0 0
0 10 0
0 0 20.
(i) The absolute column sums of C are 5+0+0 = 5 and 0 + 10 + 0 = 10and 0 + 0 + 20 = 20. The larger of these
is 20 and therefore C1 = 20
(ii).The absolute row sums of C are 5+0+0= 5 and 0+10+0 =10 and 0 + 0 + 20 =20 The larger of these is 20
and therefore C = 20
(iii) the frobinius norm is
underoot( |5|2 + |0|2 + |0|2 + |0|2 + |10|2 + |0|2 + |0|2 + |0|2 + |20|2 ) = underoot(525) =22.91
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