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If rho (A) = rho ([A|B]), then the syste...

If `rho` (A) = `rho` ([A|B]), then the system AX = B of linear equations is

A

consistent and has a unique solution

B

conistent

C

consistent and has infinitely many solution

D

inconsistent.

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The correct Answer is:
B
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PREMIERS PUBLISHERS-APPLICATIONS OF MATRICES AND DETERMINANTS -SOLUTION TO EXERCISE 1.8
  1. If A = [(2,0),(1,5)]" and B"=[(1,4),(2,0)] then |adj(AB)|=

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  2. If P = |(1,x,0),(1,3,0),(2,4,-2)| is the adjoint of 3xx3 matrix A and ...

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  3. If A = [{:(3," "1,-1),(2,-2," "0),(1," "2,-1):}] "and"" "A^(-1)=[(a(11...

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  4. If A, B and C are invertible matrices of some order, then which one of...

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  5. If (AB)^(-1)=[(12,-17),(-19,27)] "and"A^(-1)=[(1,-1),(-2,3)] "then"" "...

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  6. If A^(T).A^(-1) is symmetric, then A^(2)=

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  7. If A is a non-singular matrix such that A^(-1)=[(5,3),(-2,-1)], "then"...

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  8. A = [((3)/(5),(4)/(5)),(x,(3)/(5))] "and" A^(T)=A^(-1), then the value...

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  9. If A = [(1,tan""(theta)/(2)),(-tan""(theta)/(2),1)] and AB = I(2), the...

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  10. If A=[[cos theta,sin theta],[-sin theta,cos theta]] and A(adj A)=[[k,0...

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  11. If A=[(2,3),(5,-2)] be such that lambdaA^(-1) = A, then lambda is

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  12. If adj A=[[2,3],[4,1]] and adj B=[[1,-2],[-3,1]] then adj (AB) is :

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  13. The rank of the matrix [(1,2,3,4),(2,4,6,8),(-1,-2,-3,-4)] is

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  14. If x^(a)y^(b)=e^(m),x^(c)y^(d)=e^(n),Delta(1)=[(m,b),(n,d)]Delta(2)=[(...

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  15. Which of the following is/are correct ? (i) Adjoint of a symmetric m...

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  16. If rho (A) = rho ([A|B]), then the system AX = B of linear equations i...

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  17. If 0lt= thetalt=pi and the system of equations x+(sintheta)y- (costhet...

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  18. The augmented matrix of a system of linear equations is [(1,2,7,3),(0,...

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  19. Let A =[(2,-1,1),(-1,2,-1),(1,-1,2)] "and" 4B=[(3,1,-1),(1,3,x),(-1,1,...

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  20. If A = [(3,-3,4),(2,-3,4),(0,-1,1)], then adj (adj A) is

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