Consider the matrix
33 -10 j 9 2 74 -1 -7
A
Find a basis for the row space: Find basis for the column space of A from its columns. Write all other columns as a linear combination of the basis columns. Find a basis for the null space. Write the solution to Ax (5 4 -5 - 6)T as the sum of the homogeneous and particular solution. Find the angle between the first two column vectors.
Add a standard unit vector to the set {(3,1,4), (2,8,9)} to form a basis B' for R3. Find the transition matrix PB_B' from B = {(1,1,1), (1,2,4), (0,1,2)} to B' (show important steps). Compute the coordinate vector [w]B where w = (3,5,8) with respect to the standard basis. Use PB-B' to find [w]B'.