Question

Which of the following is equal to -4 (u + 4w) expressed as a linear combination of vectors, if u =-3i + 6j and w =3?O 3ui - 16j0 201O 20j

Answer 1

Step 1

Required: To find the value of -4( u + 4w)

Given data

`\begin{gathered} u\text{ = -3i + 6j} \\ w\text{ =-}(1)/(2)i\text{ -}(3)/(2)j \end{gathered}`

Step 2

Find the values of 4w

`\begin{gathered} 4\text{ (-}(1)/(2)i\text{ -}(3)/(2)j) \\ -2i\text{ -6j} \end{gathered}`

Step 3

Substitute for u and 4w and simplify to find the value of the given expression.

`\begin{gathered} -4\text{ ( }-3i\text{ + 6j - 2i -6j)} \\ Bring\text{ like terms together } \\ -4(\text{ -3i -2i +6j -6j)} \\ -4(\text{ -5i}) \\ =20i \end{gathered}`

Hence the final answer is 20i. The second option.