Question

Determine whether b is in the column space of A. If it is, then write b as a linear combination of the column vectors of A. (Use v1, v2, and v3, respectively, for the three columns. If not possible, enter IMPOSSIBLE.)A = [(1,3,0);(-1,1,0);(2,0,1)]b= [(2,3,-4)]

Answer 1

Answer:

b=(13/4, -27/4, -4)

Step-by-step explanation:

A.x=b

x=(a, b, c)

a   - b + 2c = 2

3a + b +  0 = 3

0  + 0 +  c = -4

solving this system

c=-4

a-b=10, 3a+b=3

a=10+b, 3(10+b)+b=3

b=-27/4

a=10-27/4

a=13/4