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Question Video: Finding the Transpose of a Column Matrix Mathematics

Find the transpose of the matrix [−5 and 4 and 4].

02:05

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.

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