# Matrix Multiplication or Inverse Problem

1. May 6, 2012

### Hypatio

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

$$\begin{pmatrix} 1 & 1 \\ 0 & 0 \\ 0 & 2 \\ 2 & 0 \\ 0 & 0 \\ \end{pmatrix} \begin{pmatrix} A \\ B \end{pmatrix}= \begin{pmatrix} 42 \\ 0 \\ 0 \\ 8 \\ 50 \\ \end{pmatrix}$$

apparently this matrix is of the form (CTC)X=CTB

3. 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.

2. May 6, 2012

### HallsofIvy

Staff Emeritus
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.

3. May 6, 2012

### Hypatio

I mistyped the Eq. Should be

$$\begin{pmatrix} 1 & 1 \\ 0 & 0 \\ 0 & 2 \\ 2 & 0 \\ 0 & 0 \\ \end{pmatrix} \begin{pmatrix} A \\ B \end{pmatrix}= \begin{pmatrix} 42 \\ 0 \\ 8 \\ 50 \\ 0 \\ \end{pmatrix}$$

4. May 6, 2012

### HallsofIvy

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

5. May 6, 2012

### Hypatio

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

6. May 6, 2012

### HallsofIvy

Staff Emeritus
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?

7. May 6, 2012

### Hypatio

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.