LINEAR ALGEBRA Chapter 4 Section 43 Question 09b Express eac

LINEAR ALGEBRA

Chapter 4, Section 4.3, Question 09b Express each vector as a linear combination of the other two. v1 (0,2,1,-1) v2E (2, 0,9, 1) v3 (1,- 7,1, 4) Click here to enter or edit your answer

Solution

V1= xv2+y v3

(0,2,1,-1)= x(2,0,9,1)+y(1,-7,1,4)

(2x+y,-7y, 9x+y, x+4y)

2x+y=0

-7y=2

Y= -2/7 and x= 1/7

V1=1/7v2. - 2/7v3

V2=xv1+ yv3

V2= x(0,2,1,-1)+y(1,-7,1,4)

(2,0,9,1)=(y,2x-7y,x+y,-x+4y)

Y=2

2x-7y=0

2x=7*2

X=7

V2=7v1+2v3

V3=xv1+ yv2

(1,-7,1,4)= x(0,2,1,-1)+ y(2,0,9,1)

(1,-7,1,4)=( 2y,2x,x+9y, -x+y)

2y=1

Y=1/2

2x=-7

X=-7/2

V3= -7/2v1+1/2v2