Answer to Question #306760 in Math for Esu

Question #306760

Let A=(2,8,5)



B=(6,0,3)




C=(4,7,9)



1.Find the vectors



a.) u=⃗



BA



2. Give examples of vectors which are parallel to u, v and w respectively.



3. Find a vector which is orthogonal to



a. u and v



4. Find the angle between and determine if they are parallel(perpendicular) or not



a. u and v



5. Find the projection of


a. u onto v



6. Find Orthogonal projection of



a. u onto v



7. Find the area of the triangle with vertices A,B and C,



8. Find the area of the parallelogram formed by


a. u and v



9.. Find the volume of the parallelpiped formed by


a. u ,v and uxv



10.Define the following Terms and give example for each



a. Symmetric Matrix



b. Skew-symmetric Matrix



c. Lower-Triangular Matrix


d. Upper Triangular Matrix



11. Write as a sum of symmetric and skew-symmetric matrices.



a.)



(


2 5 0 6 8 3 4 9 )



12. Solve the system 4 x+3 y+2 z=3



2 x+5 y+z=2



2 x+ y+6 z=5


using



a. Cramer’s rule



b. Inverse method



c. Gaussian Elimination






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