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Delta=[[1,1+ac,1+bc],[1,1+ad,1+bd],[1,1+...

`Delta=[[1,1+ac,1+bc],[1,1+ad,1+bd],[1,1+ac, 1+bc]]`

A

a+b+c

B

3

C

1

D

0

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The correct Answer is:
D
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If a, b, c are all different from zero and Delta= |[1+a,1,1],[1,1+b,1],[1,1, 1+c]|=0 , then (1)/(a)+(1)/(b)+(1)/(c)=

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Using properties of determinants prove that : |(1+a,1,1),( 1,1+b,1),(1,1,1+c)| =abc +bc +ca +ab

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Show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)| = abc(1 + 1/a + 1/b + 1/c) = abc + bc + ca + ab .

Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three column matrices satisfying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). find sin^(-1) (detA) + tan^(-1) (9det C)

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. If X and Z are of order 2xx n and 2xx p respectively and n=p then, 7 X...

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  2. Prove that {:|( b+c,a,a), ( b,c+a,b),( c,c,b+a) |:} = 4abc

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  3. Delta=[[1,1+ac,1+bc],[1,1+ad,1+bd],[1,1+ac, 1+bc]]

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  4. If (1)/(a)+(1)/(b)+(1)/(c)=0 then |[1+a, 1, 1 ],[1, 1+b, 1],[1,1,1+c]|...

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  5. If a, b, c are all different from zero and Delta= |[1+a,1,1],[1,1+b,1]...

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  6. The value of the determinant : |(1,1,1),(""^mC1,""^(m+1)C1,""^(m+2)C...

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  7. If a , b, c are all different from zero and |(1+a,1,1),(1,1+b,1),(1,...

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  8. |[77,78,79],[76,75,74],[75,74,73]|=

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  9. Delta=|[x+a,b,c],[b,x+c, a],[c,a, x+b]| which of the following is a fa...

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  10. If D=[[1,a,b],[1,b,c],[1,c,a]], then [[a,b,c],[b,c,a],[1,1,1]]=

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  11. The value of the determinant |[a1, la1+mb1, b1],[a2, la2+mb2, b2],[a3,...

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  12. If omega is a complex cube root of unit, then the value of the determi...

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  13. If alpha , beta , gamma are the roots of x^3+px+q=0 , then the value o...

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  14. If ax^(4) + bx^(3) + cx^(2) + dx + e = |{:(x^(3) + 3x , x - 1 , x+ 3) ...

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  15. Delta=|[log x ,log y, log z],[log 2 x, log 2 y, log 2 z],[log 3 x, log...

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  16. The value of the determine : Delta=|(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)| ...

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  17. The determinant: |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 if :

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  18. If f(x)=[[x-3 , 2 x^2-18 , 3 x^3-81],[ x-5 , 2 x^2-50 , 4 x^3-500],[ 1...

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  19. The value of n for which the determinant |[8 C3 , 9 C5 , 10 C7 ],[8 C4...

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  20. [[ 1 , 1 , 1],[ 4 , 3 , 2],[ 4^2 , 3^2 , 2^2 ]] =

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