Question

Let u= and a=, is u in the plane r spanned by the columns a? Why or why not?

Answer 1

To determine if u is in the plane r spanned by the columns a, we need to check if u can be expressed as a linear combination of a's columns.

Step-by-step explanation:

To determine if u is in the plane r spanned by the columns a, we need to check if u can be expressed as a linear combination of a's columns. The columns of a are a1 = i and a2 = j. So, we need to check if there exist scalars x and y such that u = x(i) + y(j).

Given that u = i + 2j, if you solve the system of equations x = 1 and y = 2, you will find that u can be expressed as a linear combination of the columns of a. Thus, u is in the plane r spanned by the columns a.