Expert answers to "A sum of scalar multiple of two or..."

beljuA

Answered question

2021-08-08

A sum of scalar multiple of two or more vectors (such as

c_{1} u + c_{2} v + c_{3} w

, where

c_{i}

are scalars) is called a linear combination of the vectors. Let

i = ⟨ 1, 0 ⟩, j = ⟨ 0, 1 ⟩, u = ⟨ 1, 1 ⟩

, and

v = ⟨ - 1, 1 ⟩

.
Express

⟨ 4, - 8 ⟩

as a linear combination of i and j (that is, find scalars

c_{1}

and

c_{2}

such that

⟨ 4, - 8 ⟩ = c_{1} i + c_{2} j

Cristiano Sears

Skilled2021-08-09Added 96 answers

Step 1
Given

i = ⟨ 1, 0 ⟩

and

j = ⟨ 0, 1 ⟩

Step 2

⟨ 4, - 8 ⟩ = 4 i - 8 j

c_{1} = 4

and

c_{2} = - 8

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