Linear Algebra Help. With multiplying matrices

Feb 2015
227
15
california
I've attached the question and solution as the answers. The problem I dont understand is number 12.

I assume the question is asking us to find Ax...In which case I got all of them wrong anyway

\(\displaystyle \begin{bmatrix} 0 & 0 & 1 \\0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{bmatrix} * \begin{bmatrix}x \\y \\z \\ \end{bmatrix} \)

Using the row form, I simply dotted each row of the matrix by vector x. I ended up with the matrix (z y x)... the solution doesnt even have the answers as variables, they have numbers which I dont understand.
For the second one I got (0 0 0), but the answers say (0 0)... how is this even possible? How can there only be 2 dimensions to that vector?

For the third one, I got (3 3 6), which is also wrong compared to the back of the book. For all of them I did it using the row multiplication (dot products).
I think I am misunderstanding the problem.Question.jpgAnswer.jpg
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey toesockshoe.

Your method seems to be ok. I think the question is probably wrong for the first one but I'd need to check the algebra for the other two.

I'm assuming A is the matrix and x is the vector in each of the three cases. (Also there is only one way to multiply all of the matrices anyway).

Can you show us your working? Additionally if you have MATLAB or Octave you can do the calculations there (except for the first one which has variables).
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
The test, as posted, is very strange. Several of the problems ask you to find "Ax" without explicitly saying what "A" and "x" are! In most of them there is only one matrix and one vector so we can assume that the A is the given matrix and x is the given vector. However, in the problem given, there are the matrix and vector you give and then two additional matrix and vector pairs. Are there three different parts to this problem?
 
Feb 2015
227
15
california
Hey toesockshoe.

Your method seems to be ok. I think the question is probably wrong for the first one but I'd need to check the algebra for the other two.

I'm assuming A is the matrix and x is the vector in each of the three cases. (Also there is only one way to multiply all of the matrices anyway).

Can you show us your working? Additionally if you have MATLAB or Octave you can do the calculations there (except for the first one which has variables).
It's a bit hard to use matrices in Latex, but Ill show you my work for the third one...

\(\displaystyle \begin{bmatrix} 2 & 1 \\ 1 & 2 \\ 3 & 3 \end{bmatrix} * \begin{bmatrix} 1 \\ 1 \end{bmatrix} \Rightarrow \begin{bmatrix} 2*1 + 1*1 \\ 1*2 + 2*1 \\ 3*1 + 3*1 \end{bmatrix} \Rightarrow \begin{bmatrix} 3 \\ 3 \\6 \end{bmatrix} \)
 
Feb 2015
227
15
california
The test, as posted, is very strange. Several of the problems ask you to find "Ax" without explicitly saying what "A" and "x" are! In most of them there is only one matrix and one vector so we can assume that the A is the given matrix and x is the given vector. However, in the problem given, there are the matrix and vector you give and then two additional matrix and vector pairs. Are there three different parts to this problem?
I assume it is a 3 part problem... the answers don't make sense though as they are all 2d vectors...while I think they should be 3d.