# What does the superscript $t$ in this matrix addition problem mean?

I know matrix addition is pretty easy - for a problem like $$\begin{bmatrix} a&b\\c&d\end{bmatrix}+\begin{bmatrix}e&f\\g&h\end{bmatrix}$$ The solution is $$\begin{bmatrix} a+e&b+f\\c+g&d+h\end{bmatrix}$$ However, I am working through some problems in this pdf and I can't seem to figure out what is meant by the following problem (pg 51, problem C10 part 3):

Let $B=\begin{bmatrix} 3&2&1\\-2&-6&5\end{bmatrix}$ and $C=\begin{bmatrix}2&4\\4&0\\-2&2\end{bmatrix}$

Find $B^t + C$.

My first thought was, oh, they're not the same shapes, so I can't add them. But it gives a solution. So what does the superscript $t$ mean?

Any help would be appreciated. Thanks!

• It is the matrix's transpose. Google it. It means rows become columns and the other way around. – DonAntonio Sep 11 '16 at 21:07

## 2 Answers

In this context, $t$ refers to the transpose of a matrix. In particular, you should find that $$B^t = \pmatrix{3&-2\\2&-6\\1&5}$$

• Ah, thank you, this makes sense. So, then, the top row becomes the first column. Okay, thanks. – heather Sep 11 '16 at 21:20

It means the matrix transpose.

In other words, just take the rows of the matrix, and make them as columns.

Example

In your case you have

$$B^T = \pmatrix{3&-2\\2&-6\\1&5}$$