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The transpose of a matrix $A$ is a matrix where the rows of $A$ become the columns of the new matrix and the columns of $A$ become its rows. For example:

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$ A= \\left( \\begin{array}{ccc} 1 & 2 & 3 \\\\ 4 & 5 & 6\\ \\end{array} \\right)$          becomes          $ A^T= \\left(\\begin{array}{ccc} 1 & 4 \\\\ 2 & 5 \\\\ 3&6\\ \\end{array} \\right)$

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The resulting matrix is called the transposed matrix of $A$ and is denoted $A^T$.

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We are asked to work out the transpose of various matrices.

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The transpose process results in rows becoming columns and columns becomimng rows.

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It may help to imagine the matrix being \"filpped\" about its diagonal.

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$A=\\var{A}$          $A^{T}=\\var{TA}$

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$B=\\var{B}$          $B^{T}=\\var{TB}$

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$C=\\var{C}$          $C^{T}=\\var{TC}$

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$D=\\var{D}$          $D^{T}=\\var{TD}$

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$E=\\var{EE}$         $E^{T}=\\var{TE}$

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Give the transpose of each matrix below.

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You will have to define the dimension of the transposed matrix before you enter your answer.

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$A=\\var{A}$               

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$A^{T}=$ [[0]]

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$B=\\var{B}$               

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$B^{T}=$ [[1]]

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$C=\\var{C}$               

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$C^{T}=$ [[2]]

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$D=\\var{D}$               

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$D^{T}=$ [[3]]

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$E=\\var{EE}$               

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$E^{T}=$ [[4]]

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