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Construct `A_(2xx3)` matrix whose elements are given by `a_(ij)=(1)/(2)|5i-3j|.` |
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Answer» `A2xx3` matrix has 2 rows and 3 columns. In general,`a2xx3` matrix is given by `A=[{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)):}]_(3xx2)` Thus, `a_(ij)=(1)/(2)|5i-3j|" where "i=1,2" and "j=1,2,3.` `:." "a_(11)=(1)/(2)|5xx1-3xx1|=(1)/(2).|2|=(1)/(2)xx2=1,` `a_(12)=(1)/(2)|5xx1-3xx2|=(1)/(2).|5-6|=(1)/(2).|-1|=(1)/(2)xx1=(1)/(2),` `a_(13)=(1)/(2)|5xx1-3xx3|=(1)/(2).|5-9|=(1)/(2).|-4|=(1)/(2)xx4=2,` `a_(21)=(1)/(2)|5xx2-3xx1|=(1)/(2).|10-3|=(1)/(2).|7|=(1)/(2)xx7=(7)/(2),` `a_(22)=(1)/(2)|5xx2-3xx2|=(1)/(2).|10-6|=(1)/(2).|4|=(1)/(2)xx4=2,` `a_(23)=(1)/(2)|5xx2-3xx3|=(1)/(2).|10-9|=(1)/(2).|1|=(1)/(2)xx1=(1)/(2).` Hence, `A=[{:(1,(1)/(2),2),((7)/(2),2,(1)/(2)):}].` |
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