Let A be a 5 x8 matrix and let rref(A) denote its reduced row echelon form. Which of the following is the following statements is always TRUEZ If the number of pivots of rref(A) equals five, then the columns space of A is R°. If rref(A) has five pivots, then the columns of A are linearly independent. If the columns 2, 3, 4, 5, and 8 of rref(A) are exactly the ones that have no pivot, then the nullity of A is 3 None of the suggested statements is is true. If columns 2, 3, and 8 of rref(A) have no pivot, then A must have 2 linearly independent rows.

Let A be a 5 x8 matrix and let rref(A) denote its reduced row echelon form. Which of the following is the following statements is always TRUEZ If the number of pivots of rref(A) equals five, then the columns space of A is R°. If rref(A) has five pivots, then the columns of A are linearly independent. If the columns 2, 3, 4, 5, and 8 of rref(A) are exactly the ones that have no pivot, then the nullity of A is 3 None of the suggested statements is is true. If columns 2, 3, and 8 of rref(A) have no pivot, then A must have 2 linearly independent rows.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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Question

Let A be a 5 x8 matrix and let rref(A) denote its reduced row echelon form. Which of the following is the following statements is always TRUEZ
If the number of pivots of rref(A) equals five, then the columns space of A is R°.
If rref(A) has five pivots, then the columns of A are linearly independent.
If the columns 2, 3, 4, 5, and 8 of rref(A) are exactly the ones that have no pivot, then the nullity of A is 3
None of the suggested statements is is true.
If columns 2, 3, and 8 of rref(A) have no pivot, then A must have 2 linearly independent rows.

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