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