Question

2.0 (1 point) 10 2.0 18 h -18 Write x as a linear combination of a and b. Use geometric reasoning and guess-and-check as necessary b. а+ x = Hints: 1. The Preview My Answer button shows the picture of x and the vector you built. 2. The coefficients only need to be specified to the 0.1's place, like "2.3". 3. Start by using small coefficients. Once your vectors are longer than about 12 units, they point right off the plot and are hard to see. If you only see the green vector, that's probably what's happening. 4. You have to match up the point at the end of the arrow on the red vector with the point of the green vector in the preview --not just put the red arrow in the middle of the green one. (The point of the arrow is where the vector points.) 5. Use the parallelogram law to do the problem geometrically. It's much more difficult to estimate the coordinates of the vectors and use row reduction.

Answer 1

We can observe that if we reverse the direction of a, ie. turn the a 180 degrees, we can see that it forms the diagonal of a parallelogram formed by the x and b. Therefore, it can be written that,

-a = x + b

or

x = -a - b

x = (-1a) + (-1b)