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Let c1,cn be scalars not all zero. Such that the following expression holds:
where ai is column vectors in Rn. Consider the set of linear equations.
Ax = B. 
where A = [a1.......an] and
 
Q. Then, Set of equations has
  • a)
    a unique solution has x = jn where j denotes n dimensional vector for all 1.
  • b)
    no solution
  • c)
    infinitely many solution
  • d)
    finitely many solution
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let c1,cnbe scalars not all zero. Such that the following expression h...
The vectors a1, a2, …, an are linearly dependent. 
For the system AX = B, 
Rank of coefficient matrix A = Rank of augmented matrix (A / B) 
= k (k< n) 
Hence, the system has infinitely many solutions. 
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Let c1,cnbe scalars not all zero. Such that the following expression holds:where aiis column vectors inRn. Consider the set of linear equations.Ax = B.where A = [a1.......an] andQ.Then, Set of equations hasa)a unique solution has x = jnwhere j denotes n dimensional vector for all 1.b)no solutionc)infinitely many solutiond)finitely many solutionCorrect answer is option 'C'. Can you explain this answer?
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