SOLUTION: Please help me solve this equation: Determine function is linear transformations. {{{ T: R^2 -> R^3 }}} T(a,b) = (a, b, a+b )

Algebra ->  Test -> SOLUTION: Please help me solve this equation: Determine function is linear transformations. {{{ T: R^2 -> R^3 }}} T(a,b) = (a, b, a+b )      Log On


   

Question 417736: Please help me solve this equation:
Determine function is linear transformations.
+T%3A+R%5E2+-%3E+R%5E3+ T(a,b) = (a, b, a+b )
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

T(m*(a, b) + n*(c, d)) = T((m*a, m*b)+(n*c, n*d))
= T(m*a + n*c, m*b + n*d)
= (m*a + n*c, m*b + n*d, m*a + n*c + m*b + n*d)
= (m*a, m*b, m*a + m*b) + (n*c, n*d, n*c + n*d)
= m*(a,b,a+b) + n*(c,d, c+d)
= m*T(a,b) + n*T(c,d).
Therefore T is a linear transformation.