No both Onto #4 Onto #22 [6 4, 0 -2, 7 6] Yes, infinite solutions only 0 solution Trivial Solution eqn = 0 One to one AND onto [7, 5] all columns have pivots [1 0 0, 0 1 0, 0 0 1] [100, 010, 001, 000] [1/3 0, -7/24, 1/8] [1/64 3/32 9/64, -15/64 13/32 -7/64, 21/64 1/32 -3/64] all rows have pivots Singular [10 01 00] cannot be one to one [9,3,5] [11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5] [100, 010, 001, 001] neither Homogeneous invalid #11 [60 248 100, 64 188 52, 68 296 124, 20 92 40] [1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2] Invertibility, most reduced form, like multiplying by 1 Ax = b has a unique solution for all b vectors, and the solution = A^-1b One to One [1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1] yes [20 72 22, 22 80 25, 16 58 18] No both Onto #4 Onto #22 [6 4, 0 -2, 7 6] Yes, infinite solutions only 0 solution Trivial Solution eqn = 0 One to one AND onto [7, 5] all columns have pivots [1 0 0, 0 1 0, 0 0 1] [100, 010, 001, 000] [1/3 0, -7/24, 1/8] [1/64 3/32 9/64, -15/64 13/32 -7/64, 21/64 1/32 -3/64] all rows have pivots Singular [10 01 00] cannot be one to one [9,3,5] [11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5] [100, 010, 001, 001] neither Homogeneous invalid #11 [60 248 100, 64 188 52, 68 296 124, 20 92 40] [1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2] Invertibility, most reduced form, like multiplying by 1 Ax = b has a unique solution for all b vectors, and the solution = A^-1b One to One [1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1] yes [20 72 22, 22 80 25, 16 58 18]
(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.
No
both
Onto #4
Onto #22
[6 4, 0 -2, 7 6]
Yes, infinite solutions
only 0 solution
Trivial Solution
eqn = 0
One to one AND onto
[7, 5]
all columns have pivots
[1 0 0, 0 1 0, 0 0 1]
[100, 010, 001, 000]
[1/3 0, -7/24, 1/8]
[1/64 3/32 9/64, -15/64 13/32 -7/64, 21/64 1/32 -3/64]
all rows have pivots
Singular
[10 01 00]
cannot be one to one
[9,3,5]
[11/40 -1/8 -7/80, -3/10 1/2 1/20, -1/5 0 1/5]
[100, 010, 001, 001]
neither
Homogeneous
invalid #11
[60 248 100, 64 188 52, 68 296 124, 20 92 40]
[1/5 0 -1/5, 3/20 1/4 -2/5, -1 0 2]
Invertibility, most reduced form, like multiplying by 1
Ax = b has a unique solution for all b vectors, and the solution = A^-1b
One to One
[1/5 0 -3/5, -4/5 1/2 19/10, 0 0 1]
yes
[20 72 22, 22 80 25, 16 58 18]