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Prove that : (i) |{:(a,c,a+c),(a+b,b,a...

Prove that :
(i) `|{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc`
(ii) Prove that : `|{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)`

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det[[a^(2),bc,ac+c^(2)a^(2)+ab,b^(2),acab,b^(2)+bc,c^(2)]]=4a^(2)b^(2)c^(2)

Prove that ,,a^(2),bc,ac+c^(2)a^(2)+ab,b^(2),acab,b^(2)+bc,c^(2)]|=4a^(2)b^(2)c^(2)

Prove that : |{:(b^(2)c^(2),bc, b+c),(c^(2)a^(2),ca, c+a),(a^(2)b^(2),ab, a+b):}|=0

Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2) .

|(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)(c-a)(a^(2)+b^(2)+c^(2))

Prove that |[-a^(2),ab,ac],[ba,-b^(2),bc],[ca,cb,-c^(2)]|=4a^(2)b^(2)c^(2)

Prove that |{:(b+c, c+a, a+b),(c+a, a+b,b+c),(a+b, b+c, c+a):}| =2(a+b+c)(ab+bc+ca-a^(2)-b^(2)-c^(2)).

Prove that: |(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^2+c^2

Prove that |[(a+b)^(2),ca,bc],[ca,(b+c)^(2),ab],[bc,ab,(c+a)^(2)]|=2abc(a+b+c)^(3)

Prove that: 2a^(2)+2b^(2)+2c^(2)-2ab-2bc-2ac=[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]

CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-FOUR MARK QUESTIONS
  1. Find the value of k, if: |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k...

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  2. If x,y and zinR, and Delta=|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x...

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  3. If |(1,a^2,a^4),(1,b^2,b^4),(1,c^2,c^4)|=k|(1,1,1),(a,b,c),(a^2,b^2,c^...

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  4. Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

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  5. |(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)...

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  6. Using properties of determinants, prove that following: |"a"+"b"+2...

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  7. |[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc

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  8. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  9. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

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  10. Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...

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  11. Given A=[(0,-1,2),(2,-2,0)]andB-[(0,1),(1,0),(1,1)]. Find the product ...

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  12. Using properties of determinants, solve the following for x: |x-2 ...

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  13. FInd x when |[x+a, a^2, a^3] , [x+b, b^2, b^3] , [x+c, c^2, c^3]|=0 wh...

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  14. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

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  15. If x=-4 is a root of a Delta=|(x,2,3),(1,x,1),(3,2,x)|=0, then find th...

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  16. Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...

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  17. prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(...

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  18. If f(x)=|a-1 0a x a-1a x^2a x a| , using properties of determinants...

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  19. If A=[(2,-1,1),(-1,2,-1),(1,-1,2)] show that A^(2)-5A+4I=0 Hence fin...

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  20. It A=[(-1,2,0),(-1,1,1),(0,1,0)] show that A^(2)=A^(-1)

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