Simplify the Matrix [[6,-3,h],[-24,12,7]]

Problem

[[6,−3,h],[−24,12,7]]

Solution

1. Identify the matrix structure and the goal of simplification, which is typically to find the Row Echelon Form (REF) using Gaussian elimination.

2. Eliminate the entry in the first column of the second row by adding a multiple of the first row to the second row.

3. Calculate the multiplier needed to turn −24 into 0 by using the pivot 6

(R_2)→(R_2)+4*(R_1)

4. Perform the row operation on each element of the second row.

−24+4*(6)=0

12+4*(−3)=0

7+4*(h)=4*h+7

5. Construct the resulting simplified matrix.

Final Answer

[[6,−3,h],[−24,12,7]]=[[6,−3,h],[0,0,4*h+7]]

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