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If [[1,1,1],[1,1+x,1],[1,1,1+y]]=0 wh...

If `[[1,1,1],[1,1+x,1],[1,1,1+y]]=0`
what are x and y?

Text Solution

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`[[1,1,1],[1,1+x,1],[1,1,1+y]]=0`
or,`[[1,0,0],[1,x,-x],[1,0,y]]=0`
`(C_2=C_2-C_1,C_3=C_3-C_2)`
or, `1[[x,-x],[0,-y]]=0`
or, xy-0=0 `rArr` x=0,or y=0
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MBD PUBLICATION-DETERMINATES-QUESTION BANK
  1. Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p...

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  2. Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c...

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  3. If [[1,1,1],[1,1+x,1],[1,1,1+y]]=0 what are x and y?

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  4. For what value fo x [[2x,0,0],[0,1,2],[-1,2,0]]=[[1,0,0],[2,3,4],[0,...

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  5. Solve [[x+a,0,0],[a,x+b,0],[a,0,x+c]]=0

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  6. Solve [[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]]=0

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  7. Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

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  8. Show that x=2 is a root of [[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]]=0 S...

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  9. Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

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  10. Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

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  11. For what value of lamda the system of equations x+y+z=6, 4x+lamda y-...

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  12. If A is a 3xx3 matrix and absA=2, then which matrix is represented by ...

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  13. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  14. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

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  15. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

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  16. Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

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  17. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  18. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  19. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  20. Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] =a^3+b^...

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