Find Reduced Row Echelon Form [[1,x,4],[3,6,8]]

Problem

[[1,x,4],[3,6,8]]

Solution

1. Identify the first pivot in the first row, which is already 1 in the first column.

2. Eliminate the entry below the first pivot by performing the row operation (R_2)−3*(R_1)→(R_2)

(R_2)−3*(R_1)=[3−3*(1),6−3*(x),8−3*(4)]

(R_2)−3*(R_1)=[0,6−3*x,−4]

[[1,x,4],[0,6−3*x,−4]]

3. Normalize the second row to create the second pivot by dividing (R_2) by 6 - 3x,a*s(s(u))*m*i*n*g - 3x \neq 0$.

1/(6−3*x)*(R_2)→(R_2)

[[1,x,4],[0,1,(−4)/(6−3*x)]]

4. Simplify the fraction in the second row.

(−4)/(6−3*x)=(−4)/(3*(2−x))=4/(3*(x−2))

[[1,x,4],[0,1,4/(3*(x−2))]]

5. Eliminate the entry above the second pivot by performing the row operation (R_1)−x*(R_2)→(R_1)

(R_1)−x*(R_2)=[1−x(0),x−x(1),4−x(4/(3*(x−2)))]

(R_1)−x*(R_2)=[1,0,4−(4*x)/(3*(x−2))]

6. Simplify the constant term in the first row.

4−(4*x)/(3*x−6)=(4*(3*x−6)−4*x)/(3*x−6)

(12*x−24−4*x)/(3*x−6)=(8*x−24)/(3*x−6)

(8*(x−3))/(3*(x−2))

Final Answer

rref*[[1,x,4],[3,6,8]]=[[1,0,(8*(x−3))/(3*(x−2))],[0,1,4/(3*(x−2))]]

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