Evaluate the determinants |{:(1,a,a^2),(...

Evaluate the determinants `|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|` .

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Evaluate : D = |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|

Without expanding the determinant, prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive then a. a b c >1 b. a b c> -8 c. a b c -2

If D=|(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)| , then D is -

The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c, k^2+c^2, 1)| is (A) k(a+b)(b+c)(c+a) (B) k a b c(a^2+b^(2)+c^2) (C) k(a-b)(b-c)(c-a) (D) k(a+b-c)(b+c-a)(c+a-b)

The value of the determinant |{:(1,,1,,1),(.^(m)C_(1),,.^(m+1)C_(1),,.^(m+2)C_(1)),(.^(m)C_(2),,.^(m+1)C_(2),,.^(m+2)C_(2)):}| is equal to

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)

If a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

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

Without expanding prove that, |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

Let p lambda^4+qlambda^3+rlambda^2+slambda+t=|{:(lambda^2+3lambda,lamb...
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The value of theta lying between theta=0 and theta=(pi)/2 and satifyi...
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Evaluate the determinants |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}| .
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Evaluate the determinants |{:(x+4,x,x),(x,x+4,x),(x,x,x+4):}|
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Let A=|{:(" "1," "sin theta,1),(-sin theta," "1,sintheta),(-1,-sinth...
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Let A be a square matrix of order 3xx3, then |KA| is equal to
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|{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha...
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|{:(x,a,b),(a,x,b),(a,b,x):}|
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|{:(2,3,4),(3,4,5),(4,5,6):}|=0
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|{:(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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|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where om...
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|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0
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|{:(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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