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For what value of x the matrix A is sing...

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

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Find the values of x , if |[3x,7], [2, 4]|=10

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

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

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

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

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

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  7. 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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  8. 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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  9. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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

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

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

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

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

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

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

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  17. If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , with...

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  18. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

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  19. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

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  20. If A is a skew-symmetric matrix of odd order n , then |A|=O .

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