Determine the standard matrix for the linear operator defined by the formula below:
T(x, y, z) = (x-y, y+2z, 2x+y+z)
The Attempt at a Solution
Because they say the "standard" matrix, they want you to use the "standard" basis, <1, 0, 0>, <0, 1, 0>, and <0, 0, 1>. What do you get when you multiply the matrix above by each of those?
You are told that T(x, y, z) = (x-y, y+2z, 2x+y+z). What is T(1, 0, 0)? What is T(0, 1, 0)? What is T(0, 0, 1)?
Compare those with the result of multiplying the matrix.
No. It might help if you actually answer the questions Halls asked you above. Those answers might lead you to the solution.So the answer would be
[x-y 0 0
0 y+2z 0
0 0 2x+y+z]
or is the answer
Yes, it doesn't make sense, and it isn't what you were asked to do.I tried to multiply the matrix
1 0 0
0 1 0
0 0 1
by the vectors given but I got this
Doesn't make sense