You are given the following information:
V is an invertible (i.e. nonsingular)3x3 matrix.
W is a noninvertible (i.e. singular) 3x3 matrix.
Xis a 4x3 matrix.
Y is a 3x4 matrix with at least one nonzero entry.
Z is a 5x3 matrix which has exactly one row that consists entirely of zeroes.
Which one of the following statements is false?
A.The rank of V is 3.
B.The rank of W is at most 2.
C.The rank of X could be 0, 1, 2 or 3.
D.The rank of Y could be 1, 2 or 3.
E.The rank of Z is 4.
Algebra Math
2014-11-21 7:51 pm
回答 (2)
2014-11-22 7:08 am
✔ 最佳答案
The answer is E.Statements A, B, C, D are correct.
I can give a counterexample to Statement E to disprove it:
Z is a 5x3 matrix which has exactly one row that consists entirely of zeroes, then Z can be
[0 0 0]
[8 8 8]
[8 8 8]
[8 8 8]
[8 8 8]
Then, clearly Z can be reduced to
[1 1 1]
[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]
which only has rank being 1, not 4.
2014-11-25 11:50 pm
The rank of matrix is ≤min(m,n). For Z, min(5,3)=3, the rank of Z cannot be as high as 4. E is the answer.
收錄日期: 2021-04-11 20:57:13
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