Construct a `2xx2` matrix, where (i) `a_("ij")=((i-2j)^(2))/(2)` (ii) `a_("ij")=|-2i+3j|`

Question

Construct a `2xx2` matrix, where (i) `a_("ij")=((i-2j)^(2))/(2)` (ii) `a_("ij")=|-2i+3j|`

Construct a `2xx2` matrix, where
(i) `a_("ij")=((i-2j)^(2))/(2)` (ii) `a_("ij")=|-2i+3j|`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

(i) We have, `A=[a_("ij")]_(2xx2)`
Such that, `a_("ij")=((i-2j)^(2))/(2)`, where `1 le ile 2, 1 le j le 2`
`:. a_(11)=((1-2)^(2))/2=1/2`
`a_(12)=((1-2xx2)^(2))/2=9/2`
`a_(21)=((2-2xx1)^(2))/2=0`
`a_(22)=((2-2xx2)^(2))/2=2`
So, `A=[(1/2,9/2),(0,2)]`
(ii) We have, `A=[a_("ij")]_(2xx2)`
Such that `a_("ij")=|-2i+3j|`, where `1 le i lt 2, 1 le j le 2`
`:. a_(11)=|-2xx1+3xx1|=1`
`a_(12)=|-2xx1+3xx2|=4`
`a_(21)=|-2xx2+3xx1|=1`
`a_(22)=|-2xx2+3xx2|=2`
`:. A=[(1,4),(1,2)]`