Could someone help me with a linear transformation question?

Question

anonymous · Answer

attachment

anonymous · Answer

sorry 0213 i do not understand

anonymous · Answer

i attached the question, i don't even know where to start

kainui · Answer

Well first off maybe make a 3x2 matrix since that's what you need to transform from 2 to 3 dimensions right? 

Then fill that matrix with 6 variables.

Then set the multiplication of the 2D vector multiplied by this variable matrix equal to the 3D vector and solve for the variables. you'll have 2 sets of equations like this, so good luck! I'll check on you in a few minutes.

anonymous · Answer

Remember that coordinate transformations can be done by multiplying by a transformation matrix--I'll call it A. Let's start out with what we know. 

|dw:1394510893764:dw|

|dw:1394510971104:dw|

We know from the rules of matrix multiplication that A must be a 3x2 matrix. This hints that we will somehow be using the two 3 dimensional column vectors we were given--but let's be more formal about it. It's been a while since I've done this, so give me a moment