24.7k views
1 vote
I need help with this question with steps need a college tutor

I need help with this question with steps need a college tutor-example-1

1 Answer

3 votes

We have that the general expression for the projection fo a vector w onto another vector v is the following:


proj_v(w)=(v\cdot w)/(v\cdot v)v

in this case, we have that v = (0,1,-3), then, if w = (x,y,z), we have that the transformation matrix is the following:


\begin{gathered} T(w)=proj_v(x,y,z)=\lbrack((x,y,z)\cdot(0,1,-3))/((0,1,-3)\cdot(0,1,-3))\rbrack v=\lbrack(0x+1y-3z)/(0+1+9)\rbrack v= \\ (y-3z)/(10)(0,-1,3)=(0,-(1)/(10)(y-3z),(3)/(10)(y-3z)) \end{gathered}

then, the transformation matrix is T(w) = (0, -1/10 (y-3), 3/10 (y-3z) )

for part b, let w = (1,2,4), then, the transformation matrix of this vector is:


\begin{gathered} T(1,2,4)=proj_v(1,2,4)=(0.-(1)/(10)(2-3(4)),(3)/(10)(2-3(4)) \\ =(0,-(1)/(10)(-10),(3)/(10)(-10))=(0,1,-3) \end{gathered}

therefore, T(1,2,4) = (0,1,-3)

User Granga
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories