Thread: Matrices (transpose with unknowns)

Matrix A=
5k 1
9 1

calculate (transpose(x)*A*x ) where x=
x1
x2
find the set of values for k where (transpose(x)*A*x ) > 0 for all non zero x in R^2

I am having real difficulty on this one, as when i did this calculation i got:

5kx1^2 + 10x1x2 + x2^2

Now it says for non-zero x but that means they can still be negative? Please help.

Originally Posted by mathsstudent8

Matrix A=
5k 1
9 1

calculate (transpose(x)*A*x ) where x=
x1
x2
find the set of values for k where (transpose(x)*A*x ) > 0 for all non zero x in R^2

I am having real difficulty on this one, as when i did this calculation i got:

5kx1^2 + 10x1x2 + x2^2

Now it says for non-zero x but that means they can still be negative? Please help.

I don't see what the confusion is ...... You require the values of k such that for all non-zero values of and .

In other words, for all non-zero values of and .

It's not hard to see that the least upper bound of is zero. Therefore .....

Alternatively, you could think of as representing a conic section ......