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

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

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Find (1)/(2)(A+A') and (1)/(2)(A-A') , when A=[(0, a, b),(-a,0,c),(-b,-c,0)]

|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|=0[where" "a neb nec]

Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}| , hence show that . |{:(0,c,b),(c,0,a),(b,a,0):}|^2=|{:(b^2+c^2," "ab," "ac),(" "ab,c^2+a^2," "bc),(" "ca," "bc,a^2+b^2):}|=4a^2b^2c^2

If |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then the value of x is -

|{:(x+a," "b," "c),(" "a,x+b," "c),(" "a," "b,x+c):}|=0

Evalute |{:(0,c,b),(c,0,a),(b,a,0):}| and hence show that, |{:(" "-a^2," "ab," "ac),(" "ab," "-b^2," "bc),(" "ca," "bc," "-c^2):}|=4a^2b^2c^2

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)= (a) A (b) B (c) I (d) A^(2)+B^(2)

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

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

|{:(a-x," "b," "c),(" "b,c-x," "a),(" "c," "a,b-x):}|=0

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

|{:(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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|{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0
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|{:(" "0," "a,b),(-a," "0,c),(-b,-c,0):}|
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|{:(9,9,12),(1,-3,-4),(1,9,12):}|=0
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|{:(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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|{:(441,442,443),(445,446,447),(449,450,451):}|=0
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Prove |{:(cos(x-a),cos(x+a),cosx),(sin(x+a),sin(x-a),sinx),(cosa tan x...
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|{:(101,103,105),(104,105,106),(107,108,109):}|=0
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|{:(5^2,5^3,5^4),(5^3,5^4,5^5),(5^4,5^6,5^7):}|=0
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|{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)...
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|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)
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|{:(1,alpha,alpha^3),(1,beta,beta^3),(1,gamma,gamma^3):}|=(alpha-beta)...
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|{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c,...
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|{:(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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|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)
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|{:(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)
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|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz
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|{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(x-4)^2
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|{:(1+a,1,1),(1,1+a,1),(1,1,1+a):}|=a^3+3a^2
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|{:(1,b+c,b^2+c^2),(1,c+a,c^2+a^2),(1,a+b,a^2+b^2):}|=(b-c)(c-a)(a-b)
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