   Chapter 11.1, Problem 66E

Chapter
Section
Textbook Problem

# a b v = a u + b w u = 〈 1 , 2 〉 w = 〈 1 , − 1 〉 . v = 〈 − 1 , 8 〉

To determine

To calculate: The value of a and b such that the vector v=1,7 can be written as au+bw, where u=1,2 and w=1,1.

Explanation

Given:

The provided vectors are v=1,7,u=1,2 and w=1,1.

Formula used:

The scalar multiple of c and u=u1,u2 is the vector cu=cu1,cu2.

The vector sum of u=u1,u2 and v=v1,v2 is the vector sum u+v=u1+v1,u2+v2

Calculation:

Let the vector v=1,7 is written as a linear combination of u=1,2 and w=1,1.

So,

v=au+bw1,7=a1,2+b1,1

Now, use the scalar multiple of a with 1,2 and b w

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