Matrix Multiplication or Inverse Problem

[Hypatio]

Homework Statement

I am more trying to figure out how to solve generally rather than solve this specific problem. Nevertheless this problem could be given as: Solve the matrix for A and B.

Homework Equations

[tex]\begin{pmatrix}
1 & 1 \\
0 & 0 \\
0 & 2 \\
2 & 0 \\
0 & 0 \\
\end{pmatrix}
\begin{pmatrix}
A \\
B
\end{pmatrix}=
\begin{pmatrix}
42 \\
0 \\
0 \\
8 \\
50 \\
\end{pmatrix}[/tex]

apparently this matrix is of the form (C^TC)X=C^TB

The Attempt at a Solution

I do not understand how to solve it! In this problem, what would A=? and B=? look like? Do I have to send the first matrix to the right-hand side?

This is just a basic example. I will later want to solve the same kind of problem where the first matrix has more columns and the second matrix has more rows.

Thank you in advance.

 

[HallsofIvy]

Do you understand what matrix multiplication is? What you have is equivalent to the 5 equations, A+ B= 42, 0= 0, 2B= 0, 2A= 8 and 0= 50. A and B have to be number for "A+ B= 42", "2B= 0", and "2A= 8" to make sense. But no matter what A and B are, "0= 50" is impossible. There is NO solution to this problem.

 

[Hypatio]

Do you understand what matrix multiplication is? What you have is equivalent to the 5 equations, A+ B= 42, 0= 0, 2B= 0, 2A= 8 and 0= 50. A and B have to be number for "A+ B= 42", "2B= 0", and "2A= 8" to make sense. But no matter what A and B are, "0= 50" is impossible. There is NO solution to this problem.

I mistyped the Eq. Should be

[tex]\begin{pmatrix}
1 & 1 \\
0 & 0 \\
0 & 2 \\
2 & 0 \\
0 & 0 \\
\end{pmatrix}
\begin{pmatrix}
A \\
B
\end{pmatrix}=
\begin{pmatrix}
42 \\
0 \\
8 \\
50 \\
0 \\
\end{pmatrix}[/tex]

 

[HallsofIvy]

So your answer is that you do not know how to multiply matrices?

 

[Hypatio]

So your answer is that you do not know how to multiply matrices?

Well, I did come to the "homework section". Maybe I should just stop trying to learn new things.

 

[HallsofIvy]

Okay, I tried to help- my point was that this problem is trivial once you multiply the matrices on the left. Can you do that?

 

[Hypatio]

Okay, I tried to help- my point was that this problem is trivial once you multiply the matrices on the left. Can you do that?

I figured it out. I kept getting nonsense so I thought I didn't know what I was doing. Turns out the values needed to be converted.