Find the coordinates of the vector 𝑥⃗ =

Question

The set

B = { < -1,-8 > , < -1,-5 > }

is a basis for ℝ^2. Find the coordinates of the vector 𝑥⃗ = < 4,29 > relative to the basis of B

[𝑥⃗ ]_B= < _ , _ >

Answer 1

x = <4, 29> = a<-1,-8> + b<-1, -5>;

-a - b = 4; (1) -8(1) + (2): 3b = -3, b = - 1; a = - 4 - b = - 4 + 1 = - 3

-8a - 5b = 29 (2)

So x = <-3, -1> in this bases.