Add [[1,2,-1,3],[2,6,1,7],[1,1,-k^2,-k]]

Problem

[[1,2,−1,3],[2,6,1,7],[1,1,−k2,−k]]

Solution

1. Identify the task as the simplification or representation of the given matrix, as "Add" in the context of a single matrix usually implies summing the rows or elements, but here it likely refers to performing row operations to reach row-echelon form.

2. Eliminate the first entry of the second row by performing the row operation (R_2)−2*(R_1)⇒(R_2)

[[1,2,−1,3],[0,2,3,1],[1,1,−k2,−k]]

3. Eliminate the first entry of the third row by performing the row operation (R_3)−(R_1)⇒(R_3)

[[1,2,−1,3],[0,2,3,1],[0,−1,−k2+1,−k−3]]

4. Eliminate the second entry of the third row by performing the row operation (R_3)+1/2*(R_2)⇒(R_3)

[[1,2,−1,3],[0,2,3,1],[0,0,−k2+5/2,−k−5/2]]

Final Answer

[[1,2,−1,3],[2,6,1,7],[1,1,−k2,−k]]⇒[[1,2,−1,3],[0,2,3,1],[0,0,(5−2*k2)/2,(−2*k−5)/2]]

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