The vector x is in a subspace H with a basis beta Find the

The vector x is in a subspace H with a basis beta = . Find the beta-coordinate vector of x. b_1 = [1, -2], b_2 = [-5 3], x = p[15 -16]

Solution

x = [15 -16];

b1 = [1 -2 ]

b2 = [-5 3];

let cordinate vector be (a,b)

then

x = a *b1 + b* b2

15 = a -5b;

-16 = -2a + 3b

a = 5, b = -2

so b (5,-2)is correct