we are given equations of vectors as
[tex]2a + 3b = 18c[/tex]
[tex]6c + d = a[/tex]
now, we want to find an expression for d in terms of the vectors a and b
so, we can eliminate c from second equation
so, we will solve for c from first equation
[tex]2a + 3b = 18c[/tex]
divide both sides by 18
we get
[tex]c=\frac{1}{9} a+\frac{1}{6} b[/tex]
now, we can plug this in second equation
[tex]6(\frac{1}{9} a+\frac{1}{6} b) + d = a[/tex]
we can simplify it
[tex]6*\frac{1}{9} a+6*\frac{1}{6} b + d = a[/tex]
[tex]\frac{2}{3} a+ b + d = a[/tex]
[tex]d = a-\frac{2}{3} a-b[/tex]
[tex]d = \frac{1}{3} a-b[/tex]..............Answer
