Find the Variables

Problem

[[1,0,1,1],[18,1,8,1],[1,0,0,1]]*[[a],[b],[c],[d]]=[[0],[0],[0]]

Solution

1. Write the system of linear equations by performing matrix multiplication.

a+c+d=0

18*a+b+8*c+d=0

a+d=0

2. Solve for a using the third equation.

a=−d

3. Substitute a into the first equation to find c

−d+c+d=0

c=0

4. Substitute a and c into the second equation to solve for b in terms of d

18*(−d)+b+8*(0)+d=0

−18*d+b+d=0

b−17*d=0

b=17*d

5. Express the solution in terms of the free variable d

a=−d

b=17*d

c=0

d=d

Final Answer

[[a],[b],[c],[d]]=[[−d],[17*d],[0],[d]]

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