# False the echelon form of a matrix with linearly

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False. The echelon form of a matrix with linearly independent columns will have a row of zeroes at the bottom, which means there is only the trivial solution. Solution or Explanation False. corresponds to and by linear independence, each A x = 0 A x = 0 corresponds to x 1 a 1 + + x n a n = 0 , and by linear independence, there exists a nontrivial solution. i = 0. = 0.
13. –/1 pointsHoltLinAlg1 2.3.044. Determine if the statement is true or false, and justify your answer. If A is a matrix with linearly independent columns, then has a solution for all A x = False. For example, if A = and b = , then A x = b has no solution. 1 1 1 0 True. The echelon form of the augmented matrix [ A b ] will not have a row of zeroes at the bottom, which means the equation has a solution. b . b , b
14. –/1 pointsHoltLinAlg1 2.3.045. Determine if the statement is true or false, and justify your answer. If is linearly independent, then so is Solution or Explanation 4 }. . . = 0. = 0. u 4 = 0 .
15. –/1 pointsHoltLinAlg1 2.3.046. Determine if the statement is true or false, and justify your answer. If is linearly dependent, then so is 4 }. . = 0. . = 0.