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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
- Find the values of x , if |3x7 2 4|=10 (ii) |x+1x-1x-3x+2|=|4-1 1 3| ...
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- Find the integral value of x , if |[x^2,x,1],[ 0, 2, 1],[ 3, 1, 4]...
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- For what value of x the matrix A is singular? A=[1+x7 3-x8] (ii) A=[x-...
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- Without expanding evaluate the determinant |41 1 5 79 7 9 29 5 3| .
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- If w is a complex cube root of unity. Show that |1w w^2w w^2 1w^2 1...
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- Show that |1a b+c1b c+a1c a+b|=0 .
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- Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .
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- Show that |1b c a(b+c)1c a b(c+a)1a b c(a+b)|=0 .
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- Without expanding prove that: |x+y y+z z+x z x y1 1 1|=0 .
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- Without expanding show that: =|cos e c^2thetacot^2theta1cot^2thetac...
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- Find the value of the determinant =|2 3 4 5 6 8 6x9x 12 x| .
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- Without expanding show that |b^2c^2b c b+cc^2a^2c a c+a a^2b^2a b a...
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- Without expanding evaluate the determinant |sinalphacosalphasin(alp...
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- Without expanding evaluate the determinant |(x^2+x^(-1))^2(a^2-a^(-1))...
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- If a ,\ b ,\ c are in A.P., find the value of |2y+4 5y+7 8y+a3y+5 6...
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- Without expanding evaluate the determinant =|265 240 219 240 225 19...
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- If 1=|1 1 1x^2y^2z^2x y z| and 2=|1 1 1y z z xx y x y z| , without exp...
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- Let =|A xx^2 1B y y^2 1C z z^2 1| and 1=|A B C x y z y z z xx y| , the...
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- If 1=|a b c x y z p q r| and 2=|q-b y-p a-x r-c z| , without expanding...
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- If A is a skew-symmetric matrix of odd order n , then |A|=O .
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