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