Question
Download Solution PDFA = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\), find (AB)T
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Transpose of a Matrix:
The new matrix obtained by interchanging the rows and columns of the original matrix is called as the transpose of the matrix.
It is denoted by A′ or AT
Calculation:
Given A = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\)
AB = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) × \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\)
AB = \(\begin{bmatrix} 1-3+0 \\ 3+6-5 \end{bmatrix}\)
AB = \(\begin{bmatrix} -2 \\ 4 \end{bmatrix}\)
∴ (AB)T = \(\begin{bmatrix} -2 & 4 \end{bmatrix}\)
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