2.Find a 2-tuple vector orthogonal to the vector [ 1 2] .
3.Find two independent vectors orthogonal to the vector [ 1 2 3]
4.Find one vector orthogonal to the vector [ 1 2 3 4]
5.Find a solution to x+2y=0. That is, find x and y that satisfy above relation. 6.Find two independent solutions to x+2y+3z=0
7.Find at least one solution to x+2y+3z+4t=0
TRUE OR FALSE:
8.All the points (vectors) in R2 (set of all real 2-tuples) constitute a vector space.
9.First quadrant of R2 where sign of all 2-tuple elements is positive is a vector space.
10.The set of points on a line passing through origin in R2 Constitute a vector space
11. The set of points (x, y) on the line x+y=1 is a vector space.
12.The set of points that satisfy Ax=b is a vector space
13.The set of points x that satisfy Ax=0 vector is a vector space. Assume that infinite solution vectors exist.
14. x+2y +3z=6; 2x+4y+5z=11. If we apply Gaussian elimination method to this problem, y will come out as free variable.
15. Problem number 14 has infinite solution.
16.Create generic integer 6x6 matrix whose rowspace and null space is same.
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