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Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,...

Evaluate `=|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]|` by two methods

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

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  2. Find the minors and cofactors of elements of the matrix A=[a(i j)]=[[1...

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  3. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by two methods

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  4. If A=[1 3 2 1] , find the determinant of the matrix A^2-2Adot

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  5. Determine the values of x for which the matrix A=[(x+1,-3 ,4),(-5,x+2,...

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  6. The value of the determinant |[x, x+y, x+2y], [x+2y, x,x+y],[x+y, x+2y...

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  7. The number of distinct real roots of |(cosecx,secx,secx),(secx, cosecx...

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  8. Let f(x)=|[cosx , x , x] , [2sinx , x , 2x] , [sinx , x , x]|, then ...

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  9. A triangle has its three sides equal to a , b and c . If the coordina...

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  10. Solve the following system of equations using Cramers rule. 5x-7y+z=1...

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  11. Let A=|(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1)|, where ...

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  12. Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(...

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  13. Prove the identity: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2...

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  14. |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A)...

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  15. Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+...

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  16. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  17. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

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  18. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

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  19. If A(x1, y1),B(x2, y2) and C(x3,y3) are vertices of an equilateral ...

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  20. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

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