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Compute the following $ \begin{bmatrix} a & b \\ -b & a \end{bmatrix} + \begin{bmatrix} a & b \\ b & a \end{bmatrix} $

1 Answer

Toolbox:
  • The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywise: $(A (+/-) B)_{i,j} = A_{i,j} +/- B_{i,j}$ where 1 ≤ i ≤ m and 1 ≤ j ≤ n.
Given:
$\begin{bmatrix}a & b\\-b & a\end{bmatrix}+\begin{bmatrix}a & b\\b & a\end{bmatrix}$
$\qquad\qquad\qquad\qquad\;=\begin{bmatrix} a+a & b+b \\ -b+b & a+a \end{bmatrix}$
$\qquad\qquad\qquad\qquad\;=\begin{bmatrix} 2a & 2b \\ 0 & 2a \end{bmatrix}$
answered Apr 12, 2013 by sharmaaparna1
 

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