Linear Operator Matrix for T Defined by Formula | Example Included

[Damascus Road]

Greetings,
can someone check if I'm doing this correctly?

I have to find the standard matrix for the linear operator T defined by the formula.

For example,

T(x1,x2,x3) = (x1 + 2x2 + x3, x1+ 5x2, x3)

Is the matrix I want just simply,

T =
1 2 1
1 5 0
0 0 1

I'm basing this on an example in my text, thanks in advance!

 

[Mark44]

Try it and see. Multiply A(x1, x2, x3)^t and see if you get (x1 + 2x2 + x3, x1 + 5x2, x3)^t.

BTW, you might notice that I renamed your matrix as A. The matrix of a transformation is different from the tranformation itself, so you shouldn't have the same name for both.