Recent content by Eleni

Homework Statement The probability that a particular computer chip fails after a hours of operation is given by 0.00005∫e^(-0.00005t)dt on the interval [a, ∝] i. find the probability that the computer chip fails after 15,000 hours of operation ii. of the chips that are still operating after...

My apologies for the absolutely horrible notation. I used the "x2" button but deleted Sub and replaced it with my values (as I have never used this type of button before.) I was very disappointed to have typed out the entire question, post it and then find that it did not make sense as it had...

Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...

Homework Statement Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)} a) Show that B1 is a basis for [R][/3] b) Find the coordinates of w=(2,3,1) relative to B1 c)Given that B2 is a basis for [R[/3], find...

Sorry to bother you again but were so helpful before. I have now come across this part (in the same question) e) Using the standard basis B={(1,0,0),(0,1,0),(0,0,1)}, find the matrix representation of T. I attempted the question by expressing the vector v=(1,2,1) with respect to the basis B. I...

Oh, that makes sense! Thank you for all your help. I have now calculated the coefficients and formed the matrix 1 2 1 0 1 -1 1 1 -3 Which has a kernel of zero (what I was looking for). I appreciate all of your suggestions. Is there an option on this site to give feedback of users...

I am thinking there is a vector missing? As the result should be a 3x3 matrix?

Thank you for your help. So my matrix should consist of the vectors, v=(1,2,1) and ui=(0,1,-1)?

I think I may have made a mistake and posted my responses within your post. I am still trying to work out this site. I apologise.

Thank you for your input, I very much appreciate it.

I have looked into it and you are correct, they don't break the commutative property of addition. Thank you for your advice.

Thank you for your help. I didn't think my calculations looked right algebraically but I rushed and wrote x1 time -x1 = -x1. I will look further into this equation. It makes sense to not swaps the "x" and "y" now that you say it. Thank you again, I appreciate the time you have taken to help.

Homework Statement Let T:[R[/3]→[R[/3] so that when u=[R][/3] and v=(1,2,1), then T(u)=u×v a) Show that T is a linear transformation. b) Find T((3,0,2)) c) Find a basis for Ker( T ). Give a geometric description of Ker( T ). Homework Equations Properties of a linear transformation: i) T(u+v)=...

Homework Statement Let V be the set of all ordered pairs of real numbers. Suppose we define addition and scalar multiplication of elements of V in an unusual way so that when u=(x1, y1), v=(x2, y2) and k∈ℝ u+v= (x1⋅x2, y1+y2) and k⋅u=(x1/k, y1/k) Show detailed calculations of one case...