Can you transpose a 3x2 matrix

Example: ie. Which is the transpose of? The transverse is the matrix where the columns are now the corresponding rows - the first column is now the first row, the second column is now the second row, etc. For a 3x2 matrix A, the transpose of A is a 2x3 matrix, where the columns are formed from the corresponding rows of A.

For a 2x4 matrix A, the transpose of A is a 4x2 matrix, where the columns are formed from the corresponding rows of A. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

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Possible Answers:. Correct answer:. Explanation : To find the transpose, we need to make columns into rows. Report an Error. Example Question 2 : The Transpose. Transpose matrix A where,. Explanation : Transposing a matrix simply means to make the columns of the original matrix the rows in the transposed matrix.

Example Question 3 : The Transpose. Example Question 4 : The Transpose. Example Question 5 : The Transpose. Example Question 6 : The Transpose. Example Question 7 : The Transpose. Example Question 8 : The Transpose. Explanation : The transverse is the matrix where the columns are now the corresponding rows - the first column is now the first row, the second column is now the second row, etc.

Example Question 9 : The Transpose. Find the transpose of matrix A. To transpose a matrix, start by turning the first row of the matrix into the first column of its transpose. Repeat this step for the remaining rows, so the second row of the original matrix becomes the second column of its transpose, and so on. This transposition is the same for a square matrix as it is for a non-square matrix. Finally, express the transposition mathematically, so if matrix B is an m x n matrix, where m are rows and n are columns, the transposed matrix is n x m, with n being rows and m being columns.

To learn how to flip square matrices over the main diagonal, keep reading! Did this summary help you? Yes No. Log in Social login does not work in incognito and private browsers. Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great.

By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article parts. Tips and Warnings. Related Articles. Article Summary. Part 1. Start with any matrix. You can transpose any matrix, regardless of how many rows and columns it has. Turn the first row of the matrix into the first column of its transpose. Repeat for the remaining rows.

The second row of the original matrix becomes the second column of its transpose. Practice on a non-square matrix. The transposition is exactly the same for a non-square matrix.

You rewrite the first row as the first column, the second row as the second column, and so forth. Express the transposition mathematically. The concept is pretty simple, but it's good to be able to describe it in mathematics. No jargon is required beyond basic matrix notation: If matrix B is an m x n matrix m rows and n columns , the transposed matrix B T is an n x m matrix n rows and m columns. Part 2. The transpose of a transpose is the original matrix.

If you switch them again, you're back where you started. Flip square matrices over the main diagonal. In a square matrix, transposition "flips" the matrix over the main diagonal. In other words, the elements in a diagonal line from element a 11 to the bottom right corner will remain the same.

Each other elements will move across the diagonal and end up at the same distance from the diagonal, on the opposite side. If you can't visualize this, draw a 4x4 matrix on a piece of paper. Now fold is over the main diagonal. See how elements a 14 and a 41 touch?

They trade places in the transpose, as does each other pair that touches when folded. Transpose a symmetric matrix. A symmetric matrix is symmetric across the main diagonal. If we use the "flip" or "fold" description above, we can immediately see that nothing changes.

All the element pairs that trade places were already identical. Part 3. Start with a complex matrix. Complex matrices have elements with a real and imaginary component.

While you can take an ordinary transpose of these matrices, most practical calculations involve the conjugate transpose instead.

Take the complex conjugate. The complex conjugate changes the sign of the imaginary components, without altering the real components. Perform this operation for all elements of the matrix. Transpose the results.