Suppose t: ℝ3→ℝ2 is a linear transformation. let u and v be the vectors given below, and suppose that t(u) and t(v) are as given. find t(3u+2v).

u =

[1]

[2]

[1]

v =

[1]

[3]

[2]

t(u) =

[−2]

[5]

t(v) =

[−2]

[7]

t(3u+2v) = ?

Step-by-step explanation:

T is a linear transformation, hence it is homogeneous (T(cr)=cT(r) for all real c and r∈ℝ³) and additive (T(r+s)=T(r)+T(s), for all r,s∈ℝ³). Apply these properties with r=3u and s=2v to obtain:

We don't have an explicit definition of T, so it's more difficult to compute T(3u+2v) directly without using these properties.

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: