Rank of 5x3 matrix A is 3, what is RREF(A)?

  • Thread starter pyroknife
  • Start date
  • #1
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Homework Statement


Matrix A is of size 5x3 (5 rows and 3 columns) with rank(A)=3. Find the reduced row echlon form of A


The Attempt at a Solution


Rank(A)=3 thus, there are 3 pivot variables. Since there are 3 pivot variables and 3 columns=> no free variables, thus we have 2 rows of zeroes at the bottom. The top 3 rows represent a 3x3 identity matrix.
[/B]
It seems like the answer is just
1 0 0
0 1 0
0 0 1
0 0 0
0 0 0
Could someone please verify?


I was curious if the question was instead a 3x5 matrix.
For this scenario I observe the following:
1) There will be 3 pivots, but since there are 5 columns, there will be 2 free variables.
2) I think RREF(A) can be 4!=4*3*2=24 different matrices?
 

Answers and Replies

  • #2
34,687
6,394

Homework Statement


Matrix A is of size 5x3 (5 rows and 3 columns) with rank(A)=3. Find the reduced row echlon form of A


The Attempt at a Solution


Rank(A)=3 thus, there are 3 pivot variables. Since there are 3 pivot variables and 3 columns=> no free variables, thus we have 2 rows of zeroes at the bottom. The top 3 rows represent a 3x3 identity matrix.
[/B]
It seems like the answer is just
1 0 0
0 1 0
0 0 1
0 0 0
0 0 0
Could someone please verify?
Sure, this is fine.
pyroknife said:
I was curious if the question was instead a 3x5 matrix.
For this scenario I observe the following:
1) There will be 3 pivots, but since there are 5 columns, there will be 2 free variables.
2) I think RREF(A) can be 4!=4*3*2=24 different matrices?
And the rank is still 3?
Actually, there will be an infinite number of matrices. There would be two columns that could have any values.
 

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