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Without expanding the determinant, prove...

Without expanding the determinant, prove that `|[41, 1, 5],[79, 7, 9], [29, 5, 3]|=0`

Text Solution

Verified by Experts

Applying `C_(1) to C_(1) -8C_(3)`, we get
`Delta = |[1, 1, 5], [7, 7, 9], [5, 5, 3]| = 0 " "[because C_(1) "and" C_(2) "are identical"]`
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RS AGGARWAL-DETERMINANTS-Exercise 6A
  1. Let A be a square matrix of order 3 x 3 Write the value of |2A| where ...

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  2. If A(i j) is the cofactor of the element a(i j) of the determinant [2-...

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  3. |(x^(2)-x+1, x-1),(x+1,x+1)|

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  4. Evaluate: |[a+ib, c+id],[-c+id, a-ib]|

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  5. Solve : (3x +4)/(7) - (x +5)/(14) = (x)/(28) + (x +1)/(14) The follo...

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  6. If |(2x,5),(8,x)|=|(6,-2),(7,3)| then the value of x is

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  7. If |[2x, x+3], [2(x+1), x+1]| = |[1, 5], [3, 3]|, find the value of x.

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  8. If A = [[3, 4],[1, 2]], find the value of 3|A|

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  9. Evaluate 2|[7, -2], [-10, 5]|

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  10. Evaluate '|[sqrt(6), sqrt(5)], [sqrt(20), sqrt(24)]|

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  11. Evaluate |[2"cos"theta, -2"sin"theta], ["sin" theta, "cos"theta]|

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  12. Evaluate |["cos" alpha, -"sin"alpha], ["sin"alpha, "cos"alpha]|

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  13. Evaluate |["sin" 60^(@), "cos"60^(@)], ["sin" 30^(@), "cos" 30^(@)]|

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  14. Evaluate |["cos" 65^(@), "sin"65^(@)],["sin"25^(@), "cos"25^(@)]|

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  15. Evaluate |["cos" 15^(@), "sin"15^(@)],["sin" 75^(@), "cos"75^(@)]|

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  16. Evaluate |[0, 2, 0], [2, 3, 4], [4, 5, 6]|

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  17. Without expanding the determinant, prove that |[41, 1, 5],[79, 7, 9], ...

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  18. For what value of x, the given matrix A = [[3-2x, x+1],[2, 4]] is a si...

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  19. Evaluate |[14, 9],[-8, -7]|

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  20. Evaluate |[sqrt(3), sqrt(5)],[-sqrt(5), 3sqrt(3)]|

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