Complexity Explorer Santa Fe Institute

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Vector and Matrix Algebra

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2.2 Matrix Operations » Quiz #10 Solution

Question 1: Recall that the transpose of a matrix simply switches the rows and columns of that matrix.  So:

\begin{bmatrix} -2 & 1 \\ 0 & 4 \end{bmatrix}^T = \begin{bmatrix} -2 & 0 \\ 1 & 4 \end{bmatrix}

 

Question 2:  (A+B)^T = \left( \begin{bmatrix} -2 & 1 \\ 0 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \right)^T = \begin{bmatrix} -2 & 2 \\ 1 & 4 \end{bmatrix}^T = \begin{bmatrix} -2 & 1 \\ 2 & 4 \end{bmatrix}

 

Question 3:   (AB)^T = \left( \begin{bmatrix} -2 & 1 \\ 0 & 4 \end{bmatrix} \begin{bmatrix}0 & 1 \\ 1 & 0 \end{bmatrix} \right)^T =\begin{bmatrix}1 & -2 \\ 4 & 0 \end{bmatrix}^T = \begin{bmatrix} 1 & 4 \\ -2 & 0 \end{bmatrix}