[20 72 22, 22 80 25, 16 58 18] [1/64 3/32 9/64, -15/64 13/32 -7/64, 21/64 1/32 -3/64] all columns have pivots [9,3,5] [10 01 00] [1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1] only 0 solution [100, 010, 001, 001] [6 4, 0 -2, 7 6] neither [100, 010, 001, 000] No [11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5] [60 248 100, 64 188 52, 68 296 124, 20 92 40] Homogeneous all rows have pivots Onto #4 [7, 5] eqn = 0 Invertibility, most reduced form, like multiplying by 1 Singular [1 0 0, 0 1 0, 0 0 1] One to One [1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2] Onto #22 yes Ax = b has a unique solution for all b vectors, and the solution = A^-1b Trivial Solution One to one AND onto invalid #11 [1/3 0, -7/24, 1/8] Yes, infinite solutions cannot be one to one both [20 72 22, 22 80 25, 16 58 18] [1/64 3/32 9/64, -15/64 13/32 -7/64, 21/64 1/32 -3/64] all columns have pivots [9,3,5] [10 01 00] [1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1] only 0 solution [100, 010, 001, 001] [6 4, 0 -2, 7 6] neither [100, 010, 001, 000] No [11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5] [60 248 100, 64 188 52, 68 296 124, 20 92 40] Homogeneous all rows have pivots Onto #4 [7, 5] eqn = 0 Invertibility, most reduced form, like multiplying by 1 Singular [1 0 0, 0 1 0, 0 0 1] One to One [1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2] Onto #22 yes Ax = b has a unique solution for all b vectors, and the solution = A^-1b Trivial Solution One to one AND onto invalid #11 [1/3 0, -7/24, 1/8] Yes, infinite solutions cannot be one to one both
(Print) Use this randomly generated list as your call list when playing the game. There is no need to say the BINGO column name. Place some kind of mark (like an X, a checkmark, a dot, tally mark, etc) on each cell as you announce it, to keep track. You can also cut out each item, place them in a bag and pull words from the bag.
[20 72 22, 22 80 25, 16 58 18]
[1/64 3/32 9/64, -15/64 13/32 -7/64, 21/64 1/32 -3/64]
all columns have pivots
[9,3,5]
[10 01 00]
[1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1]
only 0 solution
[100, 010, 001, 001]
[6 4, 0 -2, 7 6]
neither
[100, 010, 001, 000]
No
[11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5]
[60 248 100, 64 188 52, 68 296 124, 20 92 40]
Homogeneous
all rows have pivots
Onto #4
[7, 5]
eqn = 0
Invertibility, most reduced form, like multiplying by 1
Singular
[1 0 0, 0 1 0, 0 0 1]
One to One
[1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2]
Onto #22
yes
Ax = b has a unique solution for all b vectors, and the solution = A^-1b
Trivial Solution
One to one AND onto
invalid #11
[1/3 0, -7/24, 1/8]
Yes, infinite solutions
cannot be one to one
both