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