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If a1,a2,a3,……………….. are in A.P., then t...

If `a_1,a_2,a_3,………………..` are in A.P., then the value of:
`{:|(a_1,a_2,1),(a_2,a_3,1),(a_3,a_4,1)|` is equal to

A

`a_4-a_1`

B

`(a_1+a_4)/2`

C

0

D

`(a_2+a_3)/2`

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If A= diag (4, 2, 1) then det. A is equal to :

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  2. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  3. If a1,a2,a3,……………….. are in A.P., then the value of: {:|(a1,a2,1),(a...

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  4. The system of linear equations: 3x+y-z=2,x-z=1 and 2x+2y+az=5 has un...

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  5. Let I denote the 3xx3 and P be a matrix obtained by rearranging the co...

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  6. If A is matrix of order 3,such that A(adjA)=10I. Then |adjA|=

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  7. Without expanding the determinant at any stage, prove that {:|(x+1,x+2...

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  8. Consider the following statements: (i) If any two rows or coluns of a ...

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  9. Let A be a square matrix all of whose entries are integers. Which on...

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  10. Let omega ne 1 be a cube root of unity and S be the set of all non-...

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  11. Let M and N be two 3xx3 non-singular skew-=symmetric matrices such t...

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  12. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  13. The number of values of k, for which the system of equations (k""+""...

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  14. If P=[[1,alpha,3],[1,3,3],[2,4,4]] is the adjoint of a 3xx3 matrix A a...

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  15. If {:|(x,x),(1,x)| = |(3,4),(1,2)|. Write the positive value of 'x'.

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  16. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  17. If A is a square matrix order 3 such that |adjA|=225, find |A'|.

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  18. Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

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  19. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  20. Using Cofactors of elements of third column, evaluate triangle - |[1,x...

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