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Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]...

Evaluate `abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,c^2]]`

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Find the value of [[1,a,b+a],[1,b,c+a],[1,c,a+b]] .

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Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

If A=abs[[1,2,0],[1,1,0],[-1,4,0]],B=abs[[1,2,3],[1,1,-1],[4,-3,2]] and C= abs[[1,2,3],[1,1,-1],[2,2,2]] then prove that A(BC)=(AB)C

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What is the value of abs[[a,b+c,1],[b,c+a,1],[c,a+b,1]] ?

If A [[1,2,0],[1,1,0],[-1,4,0]],B=[[1,2,3],[1,1,-1],[1,1,1]]"and"C=[[1,2,3],[1,1,-1],[2,2,2]] Show that AB=AC though B !=C .Verify that: A(BC) =(AB)C

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that for any f:X rarr Y , f o idx = f =idY of.

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  2. If A=[(2,5),(1,3)], then find A^(-1)

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  3. Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,...

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  4. If [(x+y,y-z),(5-t,7+x)]=[(t-x,z-t),(z-y,x+z+t)], then find the values...

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  5. Express as a sum of a symmetric and a skew symmetric matrix: [[1,2,3],...

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  6. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  7. Find the intervals where the following functions are (a) increasing an...

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  8. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

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  9. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  10. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

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  11. Let f(x)={(absx/x,if xne0),(0,if x=0):} Examine the continuity of f(x)...

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  12. int(1+x^2)/(xsqrt(x^4+1))dx

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  13. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  14. int0^pi(xsinxdx)/(1+cos^2x)

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  15. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

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  18. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

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