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