# False the echelon form of a matrix with linearly

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the bottom, which means there is only the trivial solution.
0
Ax= 0corresponds to x1a1+ + xnan= 0, and by linear independence, there exists anontrivial solution.
Ax= 0corresponds to x1a1+ + xnan= 0, and by linear independence, each x1236i= 0.
= 0.
13.–/1 pointsHoltLinAlg1 2.3.044.Determine if the statement is true or false, and justify your answer.If Ais a matrix with linearly independent columns, then has a solution for all Ax= False. For example, if A= and b= , then Ax= bhas no solution.1110b.
b
Ab] will not have a row of zeroes at thebottom, which means the equation has a solution.
Ab] will have at least one row of zeroes at thebottom, which means the equation has a solution.
,
b
14.–/1 pointsHoltLinAlg1 2.3.045.Determine if the statement is true or false, and justify your answer.
4}.
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= 0.
= 0.
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15.–/1 pointsHoltLinAlg1 2.3.046.Determine if the statement is true or false, and justify your answer.
4}.
.
= 0.
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= 0.