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Find the values of x , if |2 4 5 1|=|2x4...

Find the values of `x` , if `|2 4 5 1|=|2x4 6x|` (ii)`|2 3 4 5|=|x3 2x5|` (iii) `|3xx1|=|3 2 4 1|`

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Verified by Experts

The correct Answer is:
i) `x= pm sqrt{3}`

ii) `x= 2`

iii) `x= pm 2sqrt{2}`


Que i.

\begin{aligned} &\left|\begin{array}{lr} 2 & 4 \\ 5 & 1 \end{array}\right|=\left|\begin{array}{cc} 2 x & 4 \\ 6 & x ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If A=[2 5 2 1] and B=[4-3 2 5] , verify that |A B|=|A||B| .

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

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  3. Find the values of x , if |2 4 5 1|=|2x4 6x| (ii)|2 3 4 5|=|x3 2x5| (...

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  4. Find the values of x , if |3x7 2 4|=10 (ii) |x+1x-1x-3x+2|=|4-1 1 3| ...

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

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  6. For what value of x the matrix A is singular? A=[1+x7 3-x8] (ii) A=[x-...

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

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  8. If w is a complex cube root of unity. Show that |1w w^2w w^2 1w^2 1...

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  9. Show that |1a b+c1b c+a1c a+b|=0 .

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  10. 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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  11. Show that |1b c a(b+c)1c a b(c+a)1a b c(a+b)|=0 .

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  12. Without expanding prove that: |x+y y+z z+x z x y1 1 1|=0 .

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  13. Without expanding show that: =|cos e c^2thetacot^2theta1cot^2thetac...

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  14. Find the value of the determinant =|2 3 4 5 6 8 6x9x 12 x| .

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  15. Without expanding show that |b^2c^2b c b+cc^2a^2c a c+a a^2b^2a b a...

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

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

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  18. If a ,\ b ,\ c are in A.P., find the value of |2y+4 5y+7 8y+a3y+5 6...

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  19. Without expanding evaluate the determinant =|265 240 219 240 225 19...

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  20. If 1=|1 1 1x^2y^2z^2x y z| and 2=|1 1 1y z z xx y x y z| , without exp...

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