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