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Prove that aI+bA+cA^(2)=A^(3), if A=[(0,...

Prove that `aI+bA+cA^(2)=A^(3)`, if `A=[(0,1,0),(0,0,1),(a,b,c)]`

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CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-FOUR MARK QUESTIONS
  1. If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify...

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  2. If A=[{:( 0,-x),(x,0):}].B[{:(0,1),(1,0):}] and x^(2)=-1 , then show ...

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  3. Prove that aI+bA+cA^(2)=A^(3), if A=[(0,1,0),(0,0,1),(a,b,c)]

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  4. If A=[[cos 2 theta, sin 2 theta],[-sin2theta, cos2theta]], find A^2

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  5. If A=[(1,-1),(2,1)], B=[(a,1),(b,-1)] and (A+B)^(2)=A^(2)+B^(2)+2AB, t...

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  6. If A=[(0,2b,c),(a,b,-c),(a,-b,c)], then find the value of a, b and c. ...

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  7. If A=[[a,b],[0,1]] then prove that A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]

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  8. 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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  9. 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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  10. 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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  11. Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

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

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

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  16. |(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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  17. 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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  18. Given A=[(0,-1,2),(2,-2,0)]andB-[(0,1),(1,0),(1,1)]. Find the product ...

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

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  20. 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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