Phoebe

2021-02-06

Let the matrix A,B, C and D be as given. Find the product of the sum of A and B and the difference between C and D.

$A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right],C=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right],D=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$

SkladanH

Skilled2021-02-07Added 80 answers

Step 1

From the given matrices,

$A+B=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]+\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]=\left[\begin{array}{cc}2& 0\\ 0& 0\end{array}\right]$

$C-D=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 2\end{array}\right]$

Step 2

Now compute the product as follows.

$(A+B)\cdot (C-D)=\left[\begin{array}{cc}2& 0\\ 0& 0\end{array}\right]\cdot \left[\begin{array}{cc}0& 0\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

Thus, the product of the sum of A and B and the difference between C and D is zero matrix.

From the given matrices,

Step 2

Now compute the product as follows.

Thus, the product of the sum of A and B and the difference between C and D is zero matrix.

Jeffrey Jordon

Expert2022-01-29Added 2605 answers

Answer is given below (on video)

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