Q3/A Prove that Ā = 4ax – 2ay – az, B = ax + 4ay – 4az are perpendicular to each other. Q3/B Answer the questions with True on the right phrase and false on the wrong phrase with correct the wrong if you found it. Answer five only 1. – sin Ø Is the result of dot product for unit vectors ā, dotāz. 2. Vector field that each point in its region is described by a magnitude as well...
Q3/A Prove that Ā = 4ax – 2ay – az, B = ax + 4ay – 4az are perpendicular to each other. Q3/B Answer the questions with True on the right phrase and false on the wrong phrase with correct the wrong if you found it. Answer five only 1. – sin Ø Is the result of dot product for unit vectors ā, dotāz. 2. Vector field that each point in its region is described by a magnitude as well...
2. Given A -4ax 2ay 3az and B 3ax 4ay az, find a. magnitude of 5A 2B b. a unit vector in the direction of (5A - 2B)/IA c. the vector component of BA that is parallel to B, and d. the vector component of A that is perpendicular to B |(5 points) a. 31.12 (5 points) b. -0.83a,-0.064ay0.54az (5 points) c. -0.807ax 1.076ay +0.269az (5 points) d. -3.19a, 3.07ay 2.73a 2. Given A -4ax 2ay 3az and B 3ax...
Let P = 2ax - 4ay + az and Q = ax + 2ay. Find R which has magnitude 4 and is perpendicular to both P and Q.
3. (15 pts.) Let A e Rmxn be a full rank matrix, m > n. Suppose that Let r = Ax-b. Prove that reprthogonal to Az minimizes llAz-b12. 3. (15 pts.) Let A e Rmxn be a full rank matrix, m > n. Suppose that Let r = Ax-b. Prove that reprthogonal to Az minimizes llAz-b12.
For the matrix A-1-4-3 2 3) consider the set 2 S-b E Rb-Ax for some xE R The vector -4 E S since -4Ax where X- The vector -3 E Ssince -3 Ay where The vector 7 E S since -7 Az where
6) Determine if vectors ã and are perpendicular to each other, prove they are using the Dot Product (show work) ā= (-60 m)X + (30 m)) + (20 m)2 b =(+4 m)X + (+2 m)9+ (+9 m)2
Problem 10.4. Prove that if akąbk € R, ax + a and bk + b, and ax <bk for all k € N, then a Sb. Problem 10.5. Prove or give a counter-example to the statement in Problem 10.4, with both replaced by <.
from the formula E(aX+b)=aE(x)+b, setting b = 0 we see that E(aX)= aE(X) Prove E(aX) = aE(x).
Assume a, b ∈ Z. Prove that if ax + by = 1 for some x, y ∈ Z, then gcd(a, b) = 1.