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EvaluateDelta=|1a b c1b c a1c a b|...

Evaluate`Delta=|1a b c1b c a1c a b|`

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To evaluate the determinant \[ \Delta = \begin{vmatrix} 1 & a & b & c \\ 1 & b & c & a \\ 1 & c & a & b \end{vmatrix} ...
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Show that |1a b_c1b c+a1c a+b|=0

The value of Delta = |(1,a,b +c),(1,b,c +a),(1,c,a +b)| , is

Evaluate the following: |[1,a, b c],[1,b, c a],[1,c, a b]|

If Delta_1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta_2=|(1,b c, a),(1,c a, b),(1,a b, c)|,t h e n (a) Delta_1+Delta_2=0 (b) Delta_1+2Delta_2=0 (c) Delta_1=Delta_2 (d) none of these

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is

Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)| .

If A_1,B_1,C_1, , are respectively, the cofactors of the elements a_1, b_1c_1, , of the determinant "Delta"=|a_1b_1c_1a_1b_2c_2a_3b_3c_3|,"Delta"!=0 , then the value of |B_2C_2B_3C_3| is equal to a1^2Δ b. a_1Δ c. a_1^2Δ d. a1 2^2Δ

Find the area of the triangle DeltaA B C in which a=1,\ b=2\ a n d\ /_c=60^0dot

NCERT ENGLISH-DETERMINANTS-All Questions
  1. Using Cofactors of elements of third column, evaluate Delta=|(1,x, y ...

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  2. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  3. EvaluateDelta=|1a b c1b c a1c a b|

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  4. Show that |a b c a+2x b+2y c+2z x y z|=0

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  5. Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

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  6. 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+...

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  7. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  8. Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

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  9. If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=...

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

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  11. Find the minor of element 6 in the determinant Delta=|1 2 3 4 5 6 7 8 ...

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  12. Find the inverse the matrix (if it exists)given in[[1, 0, 0],[ 3, 3, 0...

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  13. Find the inverse the matrix (if it exists) given in[(2, 1, 3),( 4,-1, ...

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  14. If A=((2,-3,5),(3,2,-4),(1,1,-2)) find A^(-1). Use it to solve the sys...

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  15. Find adjoint of the matrice in[(1,-1, 2),( 2, 3, 5),(-2, 0, 1)]

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  16. Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

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  17. Find adjoint of the matrice in[(1, 2),( 3, 4)]

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  18. Find the inverse the matrix (if it exists)given in[(-1, 5),(-3, 2)]

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  19. Find the inverse the matrix (if it exists)given in[(1, 2, 3),( 0, 2, 4...

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  20. Verify A (a d j A) = (a d j A) A = |A|I [(1,-1,2),(3,0,-2),(1,0,3)]

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