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From the matrix equation AB=AC, we concl...

From the matrix equation AB=AC, we conclude B=C provided.

A

A is singular

B

A is non-singular

C

A is symmetric

D

A is square

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. A and B are two non-zero square matrices such that AB = O. Then,

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  2. The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

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  3. From the matrix equation AB=AC, we conclude B=C provided.

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  4. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

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  5. The value of |(11,12,13),(12,13,14),(13,14,15)|, is

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  6. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is equal to:

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  7. If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|, then

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  8. Let a ,b , c be the real numbers. The following system of equations in...

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  9. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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  10. If omega is an imaginary cube root of unity, then the value of |(a,b o...

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  11. If alpha, beta are non - real numbers satifying x^3-1=0 then the value...

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  12. The value of the determinant |(-1,1,1),(1,-1,1),(1,1,-1)| is equal to

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  13. In a third order determinant, each element of the first column consist...

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  14. A root of the equation |[3-x,-6,3],[-6,3-x,3],[3,3,-6-x]|=0

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  15. For positive numbers x, y and z, the numerical value of the determinan...

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  16. Calculate the value of the determinant |{:(1,1,1,1),(1,2,3,4),(1,3,6,1...

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  17. if Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(5,,6,,7,,z),(x,,y,,z,,0):}|=0 ...

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  18. If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...

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  19. If a,b,and c are the side of a triangle and A,B and C are the angles o...

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  20. If [ ] denotes the greatest integer less than or equal to the real num...

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