How do I find the matrix for this linear transformation problem???

Question

R^2-------> R^3
L(x) = x1b1 + x2b2 + (x1+x2)b3
where x = (x1,x2)
b1 = (1,0,1)
b2 = (1,1,0)
b3 = (0,1,1)

Answer 1

Combine the x terms.

x1(b1 + b3) + x2(b2 + b3)
Convert this into a matrix eqaution. (x1,x2) should be a vertical vector.
| b1+b3....b2+b3 | (x1, x2)

So the first column of the matrix is b1 + b3
the second column is b2+b3.

Answer 2

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