Question

If
A = \left( {\begin{array}{*{20}{c}} 1&2&1 \\\ 3&4&2 \\\ {}&{}&{} \end{array}} \right),B = \left( {\begin{array}{*{20}{c}} 3&{ - 2}&4 \\\ 1&5&0 \\\ {}&{}&{} \end{array}} \right) ,
then find the matrix $X$ from $X + A + B = 0$ .

Answer 1

In the given question, we have been asked to find the value of ‘X’ and it is given that $X + A + B = 0$. To solve this question, we need to get ‘X’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘X’, we have to undo the matrix operations such as addition and subtraction , that has been done to the variables.

Complete step by step solution:
It is given that ,
$X + A + B = 0$
Substituting given values , we will get ,
\Rightarrow X + \left( {\begin{array}{*{20}{c}} 1&2&1 \\\ 3&4&2 \\\ {}&{}&{} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} 3&{ - 2}&4 \\\ 1&5&0 \\\ {}&{}&{} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&0&0 \\\ 0&0&0 \\\ {}&{}&{} \end{array}} \right)
Add the like terms , two matrices must have an equal number of rows and columns to be added. within which case, the sum of two matrices ‘A’ and ‘B’ are going to be a matrix which has the identical number of rows and columns as ‘A’ and ‘B’ . The sum of ‘A’ and ‘B’ , denoted ‘A+B’ , is computed by adding corresponding elements of ‘A’ and ‘B’ ,
\Rightarrow X + \left( {\begin{array}{*{20}{c}} 4&0&5 \\\ 4&9&2 \\\ {}&{}&{} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&0&0 \\\ 0&0&0 \\\ {}&{}&{} \end{array}} \right)
Now, subtract the sum ‘A+B’ from both the side of the equation,
\Rightarrow X = \left( {\begin{array}{*{20}{c}} 0&0&0 \\\ 0&0&0 \\\ {}&{}&{} \end{array}} \right) - \left( {\begin{array}{*{20}{c}} 4&0&5 \\\ 4&9&2 \\\ {}&{}&{} \end{array}} \right)
Two matrices must have an equal number of rows and columns to be subtracted. Within which case, the difference of two matrices is going to be a matrix which has the identical number of rows and columns . The difference is computed by subtracting corresponding elements ,
\therefore X = \left( {\begin{array}{*{20}{c}} { - 4}&0&{ - 5} \\\ { - 4}&{ - 9}&{ - 2} \\\ {}&{}&{} \end{array}} \right)

Note: The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.