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|{:(2,3,4),(3,4,5),(4,5,6):}|=0...

` |{:(2,3,4),(3,4,5),(4,5,6):}|=0`

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|{:(2,3,4),(1,2,5),(3,4,2):}|

|{:(5,2,3),(7,3,4),(9,4,5):}|=0

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|{:(2,3,4),(5,6,1),(3,2,3):}|

|{:(1,2,3),(4,5,6),(3,2,2):}|

If A({:(1,3,4),(3,-1,5),(-2,4,-3):})=({:(3,-1,5),(1,3,4),(+4,-8,6):}) , then A=

Verify Property 2 for Delta ={:|( 2,-3,5),(6,0,4),( 1,5,-7)|:}

Verify property 1 for Delta ={:|( 2,-3,5),(6,0,4) ,( 1,5,-7) |:}

|{:(" "1,-3,5),(-2," "4,3),(" "4," "5,6):}|

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not ? (i) R={(4,1),(5,1),(6,7)} (ii) R={(2,3),(2,5),(3,3),(6,6)} (iii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (iv) R={(1,1),(2,1),(3,1),(4,1),(5,1)}

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha...

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  2. |{:(x,a,b),(a,x,b),(a,b,x):}|

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  3. |{:(2,3,4),(3,4,5),(4,5,6):}|=0

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  4. |{:(a,b,c),(x,y,z),(p,q,r):}|=|{:(x,y,z),(p,q,r),(a,b,c):}|=|{:(y,b,q)...

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  5. |{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where om...

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  6. |{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0

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  7. |{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

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  8. |{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0

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  9. |{:(" "0," "a,b),(-a," "0,c),(-b,-c,0):}|

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  10. |{:(9,9,12),(1,-3,-4),(1,9,12):}|=0

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  11. |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c...

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  12. |{:(441,442,443),(445,446,447),(449,450,451):}|=0

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  13. Prove |{:(cos(x-a),cos(x+a),cosx),(sin(x+a),sin(x-a),sinx),(cosa tan x...

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  14. |{:(101,103,105),(104,105,106),(107,108,109):}|=0

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  15. |{:(5^2,5^3,5^4),(5^3,5^4,5^5),(5^4,5^6,5^7):}|=0

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  16. |{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)...

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  17. |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

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  18. |{:(1,alpha,alpha^3),(1,beta,beta^3),(1,gamma,gamma^3):}|=(alpha-beta)...

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  19. |{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c,...

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  20. |{:(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=(b-c)(c-a)(a-b)(bc+ca+ab)

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