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If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]] ,...

If `A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]]` , then show that `|3A|" "=" "27|A|`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  2. If A=[[2, 5], [2, 1]] and B=[[4,-3], [2, 5]] , verify that |A B|=|A||B...

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  3. If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]] , then show that |3A|" "=" "27|...

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  4. Find the values of x , if |[2, 4], [5, 1]|=|[2x,4], [6,x]|

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  5. Find the values of x , if |[3x,7], [2, 4]|=10

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  6. Find the integral value of x , if |[x^2,x,1],[ 0, 2, 1],[ 3, 1, 4]...

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  7. For what value of x the matrix A is singular? A=[[1+x,7], [3-x,8]]

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  8. Without expanding evaluate the determinant |41 1 5 79 7 9 29 5 3|

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  9. If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2,...

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  10. Show that |[1,a ,b+c],[1,b, c+a],[1,c ,a+b]|=0 .

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  11. Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

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  12. Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

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  13. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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  14. Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2th...

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  15. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

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  16. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

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  17. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

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  18. Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1...

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  19. If a ,\ b ,\ c are in A.P., find the value of |(2y+4, 5y+7, 8y+a),(3...

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  20. Without expanding evaluate the determinant =|(265, 240, 219), (240, ...

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