Simplify the Matrix [[a+d,b+e,c+f],[d,e,f],[g,h,i]]

Problem

[[a+d,b+e,c+ƒ],[d,e,ƒ],[g,h,i]]

Solution

1. Identify the structure of the matrix, noting that the first row is the sum of a vector [[a,b,c]] and the second row [[d,e,ƒ]]

2. Apply elementary row operations to simplify the expression. Specifically, subtract the second row ((R_2) from the first row ((R_1).

3. Perform the operation (R_1)→(R_1)−(R_2)

4. Calculate the new first row: (a+d)−d=a (b+e)−e=b and (c+ƒ)−ƒ=c

5. Write the resulting simplified matrix.

Final Answer

[[a+d,b+e,c+ƒ],[d,e,ƒ],[g,h,i]]=[[a,b,c],[d,e,ƒ],[g,h,i]]

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