in Linear Algebra
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2 votes
2 votes

Let  $Ax  =  b$  be  a  system  of  linear  equations  where  $A$  is  a  $m \times n$  matrix  and $b$ is a $m \times  1$  column  vector  and  $X$  is  a  $n \times 1$ column  vector  of  unknows.  Which  of  the following is false? 

  1. The system has a solution if and only if, both $A$ and the augmented matrix $[Ab]$ have the same rank.
  2. If  $m  <  n$  and  $b$  is  the  zero  vector,  then  the  system  has  infinitely  many  solutions.
  3. If $m = n$ and $b$ is non-zero vector, then the system has a unique solution.
  4. The  system  will  have  only  a  trivial  solution  when  $m  =  n,$  $b$  is  the  zero  vector  and $rank (A) = n$.
     
in Linear Algebra
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2 Answers

3 votes
3 votes
"If m=n and b is non-zero vector, then the system has a unique solution" is FALSE actuallty.
"If m=n and b is non-zero vector AND rank of matrix is also m, then the system has a unique solution" is TRUE.
0 votes
0 votes
c is correct as when m=n the matrix weill have unique soln.
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