1) Consider that, on a certain day, 495 passengers want to fly from Honolulu (HNL) to New York (JFK); 605 passengers want to fly from HNL to Los Angeles (LAX); and 1100 passengers want to fly from LAX to JFK.

All of the passengers traveling to and from LAX have direct flights, but only some of the passengers between JFK and HNL are flying direct, whereas the remainder have a layover in LAX.

Let x be the actual number of passengers who fly from HNL to JFK, let y be the total number who fly from HNL to LAX, and let z be the total number who fly from LAX to JFK.

Derive a linear system of two equations in the three unknowns (x, y, z). Use Gauss-Jordan elimination to determine the solution set.

2} Evaluate the matrix of transformation for the orthogonal projection onto the line L that passes through the origin and is in the direction Û=(3/13 , 4/13 , 12/13). Compute the rank of this matrix and explain what it tells you about the possible solutions to the system projL (x) = b for some appropriate vector b.4}

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