diff --git a/maths/assignment-matrices/assign.tex b/maths/assignment-matrices/assign.tex index 0a8478e..98cf0a9 100644 --- a/maths/assignment-matrices/assign.tex +++ b/maths/assignment-matrices/assign.tex @@ -9,20 +9,26 @@ \date{05 May, 2020} \maketitle \section{Question 1} -\[ - A = - \begin{bmatrix} - 2 & -5 & -1 \\ - -2 & -1 & 4 - \end{bmatrix} - B = - \begin{bmatrix} - 3 & 4 & 0 \\ - 5 & -2 & 3 - \end{bmatrix} -\] +If +\( +A = +\begin{bmatrix} + 2 & -5 & -1 \\ + -2 & -1 & 4 +\end{bmatrix} +B = +\begin{bmatrix} + 3 & 4 & 0 \\ + 5 & -2 & 3 +\end{bmatrix} +\) find: -\subsection{Part i} +\begin{enumerate} + \item $A + B$ + \item $2A + B$ +\end{enumerate} + +\subsection{Part 1} \[ A + B = \begin{bmatrix} @@ -37,7 +43,7 @@ 3 & -3 & 7 \end{bmatrix} \] -\subsection{Part ii} +\subsection{Part 2} \[ 2A + B = \begin{bmatrix} @@ -55,20 +61,20 @@ \section{Question 2} -\[ - A = - \begin{bmatrix} - 1 & 2 & 3 \\ - 4 & 5 & 6 \\ - 7 & 8 & 9 - \end{bmatrix} - B = - \begin{bmatrix} - 1 & 0 & 2 \\ - 2 & 1 & 2 \\ - 5 & 2 & 3 - \end{bmatrix} -\] +If \( +A = +\begin{bmatrix} + 1 & 2 & 3 \\ + 4 & 5 & 6 \\ + 7 & 8 & 9 +\end{bmatrix} +B = +\begin{bmatrix} + 1 & 0 & 2 \\ + 2 & 1 & 2 \\ + 5 & 2 & 3 +\end{bmatrix} +\), find $AB$. \[ AB = \begin{bmatrix} @@ -354,13 +360,13 @@ We know that 0 & 1 & 0 \\ 1 & 0 & 0 \end{vmatrix} - = 1 \times - \begin{vmatrix} - 0 & 1 \\ - 1 & 0 - \end{vmatrix} - = 1 \times -1 = -1 - \] + = 1 \times + \begin{vmatrix} + 0 & 1 \\ + 1 & 0 + \end{vmatrix} + = 1 \times -1 = -1 +\] \[ A^{-1} = \frac{adj.A}{|A|}