Question

Let A = a11 a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
a21 a22 a23 a24


be the coefficient matrix of a homogeneous system of linear equations in four
variables. Which of the following is/are true?

A. The system has infinitely many solutions

B. det (A) not = 0

1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.

Answer 1

only A, because 1 and 4 strings are equal

Answer 2

could you explain i lil if you dont mind?

Answer 3

B - It makes sense only for square matrixes

Answer 4

So square matrixes cant have a determinat of zero?

Answer 5

Variables will be greater than the equations and other variables can take any value ->The system has infinitely many solutions

Answer 6

A is correct for sure

Answer 7

no correct 2 and 4 equal

Answer 8

repleace 1,4 for my answer --> 2,4

Answer 9

hmm, I don't think it is possible to answer the question without some more information....

Answer 10

unfortunatley thats all the question gave me

Answer 11

bouth A and B can be true and wrong, it depends on the coeficients

Answer 12

@athe i get wht you are saying, but can an elementary matrix (square) have a determinant = 0?

Answer 13

yes

Answer 14

yes, its depends on the coefficiones. But if any coefficient =0, A -is true any case

Answer 15

@myko thanx. Oh i see what you mean, since they didnt specify the coefficients what is the general assumption in such a case?

Answer 16

there is no such a thing like general asumption. The only think true for a homogenious system is that it has at least one solution. It is called trivial solution. In this case it would be (0,0,0,0).

Answer 17

1.Only A is definatetly correct
but 2. Only B depends on the coefficient.
So does that make 3. Both A and B the right answer.

Answer 18

Yes! the trivial solution. thanx

Answer 19

myko, you're right in the general case. But this systems has infinitely many solutions for any cofficients!

Answer 20

why?

Answer 21

Because rows 2 and 4 are equal!

Answer 22

one equation too much

Answer 23

ohh, right. Didn't notice it, :). So det(A) =0 and has infinitley many solutions

Answer 24

And we have 3 equations, and 4 variables

Answer 25

Why det(A) =0 ?

Answer 26

det matrix 3x4?

Answer 27

becouse of the rows 2 and 4 being dependent

Answer 28

Of couse :) I became interested in

Answer 29

1. Only A is your answer @Kudos

Answer 30

total : A -its true

Answer 31

thanx a million guys. cheers