Video Transcript
Find the transpose of the matrix
negative five, four, four.
In this question, we are asked to
find the transpose of a matrix. And we can begin by recalling that
the transpose of a matrix switches each row of that matrix with its corresponding
column. This means that we can find the
transpose of a matrix by writing each row of the matrix as the column of a new
matrix that will be its transpose. We represent this operation with a
superscript 𝑇 as shown.
Let’s start by writing the first
row of this matrix as the first column of the transpose. We can see that there is only one
entry in the first row, so the first column of the transpose will only have this one
entry of negative five. We can repeat this process for the
second row of our matrix. This row only contains the entry
four. We need to write this as the second
column in the transpose, so we have a second column only containing four. We can apply this process to the
final row of the matrix. We write this row as the final
column in the transpose. It is only the entry four. Since this is the final row, we can
say the transpose of this matrix is the one-by-three matrix negative five, four,
four.
A useful check to make when finding
transposes is to recall that the transpose switches the number of rows and columns a
matrix has. So, we can note that the given
matrix has three rows and one column. This means that when we take the
transpose of this matrix, we switch these numbers around. So we must have a matrix with one
row and three columns.
This agrees with our answer. So we can conclude the transpose of
the three-by-one matrix negative five, four, four is the one-by-three matrix
negative five, four, four.
