decide whether each of the following is true or false

a. a system of linear equations could have exactly two solutions

b. a system of linear equations could have an infinite number of solutions

c. if A and B are matrices, then AB is always equal to BA
I think this is true

d. if f and g are functions then (fog)(x) is always equal to (gof)(x)
I think this is false

Question

decide whether each of the following is true or false

a. a system of linear equations could have exactly two solutions

b. a system of linear equations could have an infinite number of solutions

c. if A and B are matrices, then AB is always equal to BA
I think this is true

d. if f and g are functions then (fog)(x) is always equal to (gof)(x)
I think this is false

anonymous · Answer

@uri @ninjasandtigers

jim_thompson5910 · Answer

AB = BA is not true in general

matrix multiplication is not commutative

jim_thompson5910 · Answer

same for (f o g) and (g o f)

function composition is also not commutative

anonymous · Answer

hmm ok... what about the first two?

anonymous · Answer

a linear equation can have no solutions, one solution, or infinitely many solutions

anonymous · Answer

but not two?

anonymous · Answer

@ninjasandtigers

anonymous · Answer

nope