In Exercises 13 and 14, find the best approximation to z by vectors of the form c 1 v 1 + c 2 v 2 . 14. z = [ 2 4 0 − 1 ] , v 1 = [ 2 0 − 1 − 3 ] , v 2 = [ 5 − 2 4 2 ]
In Exercises 13 and 14, find the best approximation to z by vectors of the form c 1 v 1 + c 2 v 2 . 14. z = [ 2 4 0 − 1 ] , v 1 = [ 2 0 − 1 − 3 ] , v 2 = [ 5 − 2 4 2 ]
Solution Summary: The author explains that the best approximation of z is left[c1 0
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find the best approximation to z by vectors of the form c1v1 + c2v2.
Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of x3. How does its length compare with the sum of the lengths of x1 and x2?
In Exercises 57-62, compute the angle between the two planes, defined asthe angle 0 (between O and n) between their normal vectors (Figure 10).59. 2x + 3y + 1z = 2 and 4x - 2y + 2z = 4
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