Question

A homogeneous system of linear equations consists of six equations in five variables (i.e. unknowns). The rank of the coefficient matrix is 2. How many solutions does this system have?

Answer 1

infinite

Answer 2

But the textbook says a homogenous linear system with more unknowns than equations has infinetly solutions. This one has 5 unknowns and 6 equations. It's less.

Answer 3

depend on the rank of augmented matrix. the rank of it is 2, that means you have 2 linearly independent equations, (just 2) and you have 5 variables. now, compare 2 and 5 which is bigger?

Answer 4

My choices are:
A.The system has no solution.
B.The system has only the trivial solution.
C.The system has a two-parameter family of solutions.
D.The system has a three-parameter family of solutions.
E.The system has a four-parameter family of solutions.

Answer 5

for example: x +y =5
2x +2y = 10
3x +3y = 15
the rank of the system is 1 although you have 3 equations and 2 unknowns. so, the solution is infinite set

Answer 6

in your particular case, 2 equations, 5 unknowns --> 3 free variables or 3 parameters
Pick the choice, which one?? That's just terminology.

Answer 7

So it's D

Answer 8

I said 2 equations . it means 2 linearly independent equations
Yes, I think so . It's D

Answer 9

Thank u!!!

Answer 10

np