If `X=[{:( 3,1,-1) ,(5,-2,-3) :}] "and" Y= [{:( 2,1,-1),( 7,2,4):}]` then find (i) x+y, (ii) 2x-3y. (iii) a matrix Z such that `X+Y+Z` is a zero matrix.

If `X=[{:( 3,1,-1) ,(5,-2,-3) :}] "and" Y= [{:( 2,1,-1),( 7,2,4):}]` t

1.	If `X=[{:( 3,1,-1) ,(5,-2,-3) :}] "and" Y= [{:( 2,1,-1),( 7,2,4):}]` then find (i) x+y, (ii) 2x-3y. (iii) a matrix Z such that `X+Y+Z` is a zero matrix.
Answer» We have , `X=[{:(3,1 ,-1) ,(5,-2,-3):}]_(2xx3) "and" =[{:(2,1,-1),(7,2,4):}]_(2xx3)` (i) `x+y=[{:(3+2,1+1,-1-1),(5+7,-2+2,-3+4):}]=[ {:(5,2,-2) ,(12,0,1):}]` `because 2x=2[{:( 3,1,-1),(5,-2,-3) ,(5,-2,-3):}]=[{:(6, 2,-2) ,(10,-4,-6):}]` and `3Y=3[{:(2,1,-1),(7,2,4):}] =[{:(6,3,-3),(21,6,12):}]` `therefore 2X-3Y=[{:(6,-6,2-3,-2+3),(10-21,,-4-6,-6-12):}]=[{:(0,-1,1),(-11,-10,- 18) :}]` (iii) `X+Y=[{:(3+2,1+1,-1-1),(5+7,-2+ 2,-3+4):}]=[{:(5,2,-2),(12,0,+1):}]` Also, `X+Y+Z=[{:(0,0,0),(0,0,0):}]` We see that Z is the additive inverse of (X+y) or negative or (X+Y) `Z=[{:(-5,- 2,2),(-12,0,-1):}] [because Z=-(X+Y)]`

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If `X=[{:( 3,1,-1) ,(5,-2,-3) :}] "and" Y= [{:( 2,1,-1),( 7,2,4):}]` then find (i) x+y, (ii) 2x-3y. (iii) a matrix Z such that `X+Y+Z` is a zero matrix.

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