Question

(Matrix) addiction and subtraction of a matrix

calculate:
A) A+B+C
B) A-B-C
C) A+B-C

Answer 1

See explanation

Explanation:

When we add or subtract matrices with the same dimensions, we simply add or subtract corresponding elements.

A.

`A+B+C\\ \\=\left(\begin{array}{ccc}2&0&-1\\-4&1&3\end{array}\right)+\left(\begin{array}{ccc}0&-1&2\\5&0&6\end{array}\right)+\left(\begin{array}{ccc}-7&5&-2\\-6&-9&-11\end{array}\right)\\ \\=\left(\begin{array}{ccc}2+0+(-7)&0+(-1)+5&-1+2+(-2)\\-4+5+(-6)&1+0+(-9)&3+6+(-11)\end{array}\right)\\ \\=\left(\begin{array}{ccc}-5&4&-1\\-5&-8&-2\end{array}\right)`

B.

`A-B-C\\ \\=\left(\begin{array}{ccc}2&0&-1\\-4&1&3\end{array}\right)-\left(\begin{array}{ccc}0&-1&2\\5&0&6\end{array}\right)-\left(\begin{array}{ccc}-7&5&-2\\-6&-9&-11\end{array}\right)\\ \\=\left(\begin{array}{ccc}2-0-(-7)&0-(-1)-5&-1-2-(-2)\\-4-5-(-6)&1-0-(-9)&3-6-(-11)\end{array}\right)\\ \\=\left(\begin{array}{ccc}9&-4&-1\\-3&10&8\end{array}\right)`

C.

`A+B-C\\ \\=\left(\begin{array}{ccc}2&0&-1\\-4&1&3\end{array}\right)+\left(\begin{array}{ccc}0&-1&2\\5&0&6\end{array}\right)-\left(\begin{array}{ccc}-7&5&-2\\-6&-9&-11\end{array}\right)\\ \\=\left(\begin{array}{ccc}2+0-(-7)&0+(-1)-5&-1+2-(-2)\\-4+5-(-6)&1+0-(-9)&3+6-(-11)\end{array}\right)\\ \\=\left(\begin{array}{ccc}9&-6&3\\7&10&20\end{array}\right)`