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By using properties of determinants, pro...

By using properties of determinants, prove that
`|[0,a ,-b],[-a,0,-c],[b,c,0]|=0`

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`|[0,a ,-b],[-a,0,-c],[b,c,0]|=0 [because[[0,a ,-b],[-a,0,-c],[b,c,0]]`is a skew-symmetricmatrixof order 3
Determinant of a skew-symmetric matrix of odd order is zero.
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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Without expanding the determinant prove the following. |[1,bc,a(b+c)...

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  2. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  3. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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  4. By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^...

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  5. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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  6. Using properties of determinants prove the following. abs[[1,1,1],...

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  7. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

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  8. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

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  9. By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],...

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  10. Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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  11. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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  12. Using properties of determinants prove the following. abs[[1,x,x^2...

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  13. By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-...

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  14. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  15. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  16. Which of the following is correct?

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  17. Consider a triangle whose vertices are (3,8),(-4,2) and (5,1) Find are...

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  18. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  19. Find the adjoint of A= [(1,2),(3,4)]

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  20. Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]

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