Find the transpose of the matrix: [ rr 1 & -1 2 & 3 ] - Vidyadip

Question

Find the transpose of the matrix: $\left[\begin{array}{rr} {1} & {-1} \\ {2} & {3} \end{array}\right]$

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Answer

We know that transpose of a matrix is obtained by interchanging the elements of the rows and columns. In other words, we can say, if
$\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{m \times \mathrm{n}} \text { then } \mathrm{A}^{\prime}=\left[\mathrm{a}_{\mathrm{ji}}\right]_{\mathrm{n\times m}}$
So, let $B =$$\left[\begin{array}{cc} {1} & {-1} \\ {2} & {3} \end{array}\right]$
Therefore, transpose of the given matrix B denoted by B’ is given by
$ B' $= $\left[\begin{array}{cc} {1} & {2} \\ {-1} & {3} \end{array}\right]$
So,Transpose of the given matrix is $\left[\begin{array}{cc} {1} & {2} \\ {-1} & {3} \end{array}\right]$

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