Compute the coordinates of the point (1, 1) in the basis formed by the columns of AB. Express your computation abstractly in terms of A and B before you use the specific A and B given above.

Use the Cauchy-Schwarz inequality

|v · w| ≤ ||v|| · ||w||

to prove the Triangle Inequality

||v + w|| ≤ ||v|| + ||w||.

(Hint: Begin by computing ||v + w||2 with dot products, and then plug in the

Cauchy-Schwarz inequality when the opportunity arises.)

Solution.

||v + w||2 = (v + w) · (v + w)

= v · v + v · w + w · v + w · w

= ||v||2 + 2(v · w) + ||w||2

≤ ||v||2 + 2||vw|| + ||w||2 by the C.S. Inequality

= (||v|| + ||w||)

2

Taking the square root of both sides, we conclude that

||v + w|| ≤ ||v|| + ||w||Step-by-step explanation:

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

i believe the answer is d.

hope it you! : d