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.