Answer to Question #340744 in Linear Algebra for connor

Question #340744

Consider the real space R3


 The following vectors form a basis S of R3:


u1 = (1, −1, 0), u2 = (1, 1, 0), u3 = (0, 1, 1)


Find the coordinate vector [v] of v = (5, 3, 4) relative to the basis S .


1
Expert's answer
2022-05-16T10:27:11-0400

Let

"\\vec v=a\\vec{u_1}+b\\vec{u_2}+c\\vec{u_3}"

Then


"a+b=5"

"-a+b+c=3"

"c=4"

We have


"a+b=5"

"2b+c=8"

"c=4"

Then


"a=3"

"b=2"

"c=4"

Vector "\\vec{v}" has the coordinates "\\langle 3,2,4\\rangle" relative to the basis S.


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