Question 3, Exercise 2.2

Solutions of Question 3 of Exercise 2.2 of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

If $A=\left[\begin{array}{ccc}3 & -1 & 2 \\ 0 & 6 & 1 \\ -1 & 0 & -3\end{array}\right]$ and $B=\left[\begin{array}{ccc}2 & 1 & 7 \\ 0 & 2 & -1 \\ -3 & 4 & 2\end{array}\right]$ then find a matrix $C$ such that: $A+B+C=0$

Solution.

Given $$A+B+C=0,$$ this given $$C=-A-B.$$ Thus \begin{align*} C&=-\begin{bmatrix}3 & -1 & 2 \\ 0 & 6 & 1 \\ -1 & 0 & -3\end{bmatrix}-\begin{bmatrix}2 & 1 & 7 \\ 0 & 2 & -1 \\ -3 & 4 & 2\end{bmatrix}\\ &=\begin{bmatrix}-3-2 & 1-1 & -2-7 \\ 0-0 & -6-2 & -1+1 \\ 1+3 & 0-4 & 3-2\end{bmatrix}\\ &=\begin{bmatrix}-5 & 0 & -9 \\ 0 & -8 & 0 \\ 4 & -4 & 1\end{bmatrix}\\ \end{align*}

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