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By using properties of determinants, pro...

By using properties of determinants, prove that
`|[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k)`

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`|[y+k,y,y],[y,y+k,y],[y,y,y+k]|`
`|[3y+k,y,y],[3y+y,y+k,y],[3y+y,y,y+k]|(byC_1rarrC_2+C_3)`
`=(3y+k)|[1,y,y],[1,y+k,y],[1,y,y+k]|`
`(3y+k)|[1,y,y],[0,k,0],[0,0,k]|`(by `R_2rarrR_2-R_1`and`R_3rarrR_3-R_1`)
`=(3y+k)k^2=k^2(3y+k)`
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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

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  2. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

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  3. By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],...

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  4. Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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  5. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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  6. Using properties of determinants prove the following. abs[[1,x,x^2...

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  7. By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-...

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  8. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  9. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  10. Which of the following is correct?

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  11. Consider a triangle whose vertices are (3,8),(-4,2) and (5,1) Find are...

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  12. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  13. Find the adjoint of A= [(1,2),(3,4)]

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  14. Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]

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  15. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  16. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  17. Find the inverse of the following matrics. [[2,-2],[4,3]]

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  18. Find the inverse of the following matrics. [[-1,5],[-3,2]]

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  19. Find the inverse of the following A=[[1,2,3],[0,2,4],[0,0,5]]

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  20. Find the inverse of the following A=[[1,0,0],[3,3,0],[5,2,-1]]

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