InterviewSolution
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InterviewSolution
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Solve the following equations for X and Y : `2X-Y=[(3,-3,0),(3,3,2)], 2Y+X=[(4,1,5),(-1,4,-4)]` |
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Answer» Given `2X-Y=[{:(3,-3,0),(3,3,2):}]` on multiplying both sides by 2, we get `4x-2y=2[{:(3,-3,0),(3,3,2):}], 4x-2y=[{:(6,-6,0),(6,6,4):}]` also given `x+2y= [{:(4,4,4),(-1,4,-4):}]` Adding Eqs. (i) and (ii) , we get `5X=[{:(6,-6,0),(6,6,4):}]+[{:(4,1,5),(-1,4,-4):}]` `= [{:(6+4,-6+1,0+5),(6-1,6+4,4-4):}]=[{:(10,-5,5),(5,10,0):}]` `X=(1)/(5)[{:(10,-5,5),(5,10,0):}]rArr X=[{:(2,-1,1),(1,2,0):}]` putting the value of X in Eq. (ii), we get `[{:(2,-1,1),(1,2,0):}]+2Y=[{:(4,1,5),(-1,4,-4):}]` `rArr 2Y = [{:(4,1,5),(-1,4,-4):}]-[{:(2,-1,1),(1,2,0):}]` `=[{:(4-2,1+1,5-1),(-1-1,4-2,-4-0):}]=[{:(2,2,4),(-2,2,-2):}]` `Y = [{:(1,1,2),(-1,1,-2):}]` Hence, `X = [{:(2,-1,1),(1,2,0):}] and Y= [{:(2,-1,1),(-1,1,-2):}]` |
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