Transpose of a column matrix is

By Mandeep Kumar|Updated : September 27th, 2022

(a) zero matrix

(b) diagonal matrix

(c) column matrix

(d) row matrix

Transpose of a column matrix is row matrix. We can write it as AT = [aij]n x m. The matrix obtained by interchanging the rows and columns is called the transpose matrix.

Transpose of a Column Matrix

If A = [aij]m x n, then interchange the rows and columns to obtain the matrix of A is called the transpose of A, denoted by A′ or (AT). AT = [aij]n x m

  • A = 1

               2

               3

  • AT = 1 T = [1 2 3]

                 2

                 3

As a result, a row matrix can be transformed into a column matrix, and a column matrix can be transformed into a row matrix.

Summary:

Transpose of a column matrix is (a) zero matrix (b) diagonal matrix (c) column matrix (d) row matrix

Row matrix is the transpose of a column matrix which is denoted as AT = [aij]n x m. Transpose of the matrix A is represented as A′ or (AT). It can be also written as, if A = [aij]m×n, then AT = [aji]n×m.

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