New Jersey native trees

some matrices and their reduced row echelon forms

 
PINE (5 by 4)   
(1  2  4 1) {1 0 0  3) 
(1  1  2 2) (0 1 0 -5) 
(0  2  5 0)~(0 0 1  2) 
(0 -2 -4 2) (0 0 0  0) 
(2  1  0 1) (0 0 0  0)
 
BIRCH (4 by 5)   
(1 1 0  0 2) {1 0 0 -2  3) 
(2 1 2 -2 1)~(0 1 0  2 -1)
(4 2 5 -4 0) (0 0 1  0 -2) 
(1 2 0  2 1) (0 0 0  0  0)
 
SYCAMORE (4 by 3)   
(-2 1  1) (1 0 -1/5) 
(-4 2  2)~(0 1  3/5) 
( 8 1 -1) (0 0    0) 
(-7 1  2) (0 0    0)
 
HICKORY (3 by 4)   
(-2 -4  8 -7) (1 2 0  3/2)
( 1  2  1  1)~(0 0 1 -1/2)
( 1  2 -1  2) (0 0 0    0)
 
OAK (4 by 5)   
(0  2  5  2 0) {1 0 0 -3 -3)
(2 -1  1  0 1)~(0 1 0 -4 -5)
(1  0  2  1 1) (0 0 1  2  2) 
(1 -1 -1 -1 0) (0 0 0  0  0)
 
CEDAR (5 by 4)   
(0  2 1  1) {1 0 0  0)
(2 -1 0 -1) (0 1 0  1)
(5  1 2 -1)~(0 0 1 -1)
(2  0 1 -1) (0 0 0  0)
(0  1 1  0) (0 0 0  0)
 
WILLOW (3 by 4)   
(3 5 -1| a) (1 0 -11/8 |  {3/4}a-{5/8}b) 
(2 6  1| b)~(0 1   5/8 | -{1/4}a+{3/8}b) 
(4 4 -3| c) (0 0     0 |        -2a+b+c)
 
ALDER (3 by 4)   
( 3 2  4| a) (1 0  2|    (3/4)a-(1/4)b) 
( 5 6  4| b)~(0 1 -1|   -(5/8)a+(3/8)b)
(-1 1 -3| c) (0 0  0| (11/8)a-(5/8)b+c)
 
REDBUD (3 by 4)   
( 2 -3  5| a) (1 0 0|  -(3/25)a-(4/25)b+{1/25)c) 
(-7  1 -2| b)~(0 1 0| (43/25)a-(1/25)b-(31/25)c)
( 3 -5  7| c) (0 0 1| (32/25)a+(1/25)b-(19/25)c)
 
ASH (3 by 4)   
( 2 -7  3| a) (1 0 0| -(3/25)a+(43/25)b+(32/25)c) 
(-3  1 -5| b)~(0 1 0|   -(4/25)a-(1/25)b+(1/25)c)
( 5 -2  7| c) (0 0 1| (1/25)a-(31/25)b -(19/25)c)
Correction A printed - sign should have been a + sign. That correction has been
made above, and I thank Mr. Wilson.