One to One [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] invalid #11 [6 4, 0 -2, 7 6] Singular [9,3,5] neither Invertibility, most reduced form, like multiplying by 1 all rows have pivots No One to one AND onto Yes, infinite solutions Trivial Solution Homogeneous [60 248 100, 64 188 52, 68 296 124, 20 92 40] Onto #4 [100, 010, 001, 000] [7, 5] eqn = 0 only 0 solution Onto #22 [1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2] all columns have pivots [1 0 0, 0 1 0, 0 0 1] [11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5] [1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1] [1/3 0, -7/24, 1/8] both [10 01 00] [100, 010, 001, 001] Ax = b has a unique solution for all b vectors, and the solution = A^-1b yes cannot be one to one One to One [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] invalid #11 [6 4, 0 -2, 7 6] Singular [9,3,5] neither Invertibility, most reduced form, like multiplying by 1 all rows have pivots No One to one AND onto Yes, infinite solutions Trivial Solution Homogeneous [60 248 100, 64 188 52, 68 296 124, 20 92 40] Onto #4 [100, 010, 001, 000] [7, 5] eqn = 0 only 0 solution Onto #22 [1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2] all columns have pivots [1 0 0, 0 1 0, 0 0 1] [11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5] [1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1] [1/3 0, -7/24, 1/8] both [10 01 00] [100, 010, 001, 001] Ax = b has a unique solution for all b vectors, and the solution = A^-1b yes cannot be one to one
(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.
One to One
[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]
invalid #11
[6 4, 0 -2, 7 6]
Singular
[9,3,5]
neither
Invertibility, most reduced form, like multiplying by 1
all rows have pivots
No
One to one AND onto
Yes, infinite solutions
Trivial Solution
Homogeneous
[60 248 100, 64 188 52, 68 296 124, 20 92 40]
Onto #4
[100, 010, 001, 000]
[7, 5]
eqn = 0
only 0 solution
Onto #22
[1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2]
all columns have pivots
[1 0 0, 0 1 0, 0 0 1]
[11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5]
[1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1]
[1/3 0, -7/24, 1/8]
both
[10 01 00]
[100, 010, 001, 001]
Ax = b has a unique solution for all b vectors, and the solution = A^-1b
yes
cannot be one to one