Matrices A and B are row equivalent. Choose one mathematical statement that can be made concerning the properties of the matrix 0 -7 -71 4 -7 -7 -6 1 11 1 0.5 -1.5 A = B = 0 -4.95 -4.75 0 0.0404 7 -5 10 19 -1 3 -1. Selected Answer: A is invertible because there are no rows of all zeros in B. Answers: A is invertible because there are no rows of all zeros in B. A is not invertible because B has no free variables. A is invertible because A has four pivots. All of the above. None of the above.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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I got this question wrong on a quiz.  Can you explain why "A is invertible because there are no rows of all zeros in B" isn't true?  

After studying some more, I think the correct answer would be "A is invertible because A has four pivot points".  I'm just not sure why "A is invertible because there are no rows of all zeros in B" is not a valid choice as well.

Matrices A and B are row equivalent. Choose one mathematical statement that can be made concerning the properties of the matrix
0 -7 -71
4
-7
-7
-6
1 11
1
0.5
-1.5
A =
B =
0 -4.95 -4.75
0 0.0404
7 -5 10 19
-1
3 -1.
Selected Answer:
A is invertible because there are no rows of all zeros in B.
Answers:
A is invertible because there are no rows of all zeros in B.
A is not invertible because B has no free variables.
A is invertible because A has four pivots.
All of the above.
None of the above.
Transcribed Image Text:Matrices A and B are row equivalent. Choose one mathematical statement that can be made concerning the properties of the matrix 0 -7 -71 4 -7 -7 -6 1 11 1 0.5 -1.5 A = B = 0 -4.95 -4.75 0 0.0404 7 -5 10 19 -1 3 -1. Selected Answer: A is invertible because there are no rows of all zeros in B. Answers: A is invertible because there are no rows of all zeros in B. A is not invertible because B has no free variables. A is invertible because A has four pivots. All of the above. None of the above.
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