Problems:

1.For vectors and , we have What are the largest and smallest values possible for and ?

2.Prove that the matrix A and [A AB] have the same column space.

3.Suppose A is a 5*4 matrix with rank 4. Prove that Ax = b has no solution when the 5*5 matrix [A b] is invertible, and Ax = b is solvable when [A b] is singular.

4.Suppose A is a 3*3 matrix and it satisfies . Prove that det(A) = 0.

5.(Matlab) Given 13 two-dimensional data points as: x = [0 2 4 6 8 10 12 14 16 18 20 22 24], y = [15 14 14 16 20 23 26 27 26 25 22 18 16]. Do the least square regression fi

Problemsw 1. For vectors a and b, we have \"all : 6, \"b\" : 3. What are the largest and smallest values possible for Ila b\" and (if!) ?