Question

What is the transpose in matrix ?

Answer 1

Answer:

⚡The transpose of a matrix is simply a flipped version of the original matrix. We can transpose a matrix by switching its rows with its columns.

⚡Let us now go back to our original matrices A and B. Though they have the same set of elements, are they equal?

The answer is no. That’s because their order is not the same. Now, there is an important observation. There can be many matrices which have exactly the same elements as A has.

Here, the number of rows and columns in A is equal to number of columns and rows in B respectively. Thus, the matrix B is known as the Transpose of the matrix A. The transpose of matrix A is represented by A′ or AT. The following statement generalizes transpose of a matrix:

If A = [aij]m×n, then A′ =[aij]n×m.

Thus Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given matrix into columns and vice-versa.”

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Answer 2

Step-by-step explanation:

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by Aᵀ.

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