Special Homework Problem due Thursday, Oct 21: Let M be the 5x5 real matrix, J - 2I = -1 +1 +1 +1 +1 +1 -1 +1 +1 +1 +1 +1 -1 +1 +1 +1 +1 +1 -1 +1 +1 +1 +1 +1 -1 Factor this matrix into an orthogonal matrix, Q, and an upper triangular matrix, R. /* This matrix is related to Textbook Problem 4.4.17 */ In order to ease the grader's work, try to conform to the following notational conventions: Let the five columns of M be M = a|b|c|d|e Let the five columns of Q be q1, q2, q3, q4, and q5. Let any preliminary (unnormallized) scalar multiples of these column vectors be denoted by q1', q2', etc Avoid drifting far off course by CHECKING YOUR WORK at each stage: Is your q1^T q1 = 1 ? Does your q2' satisfy q1^T q2' = 0? Is your q2^T q2 = 1 ? Does your q3' satisfy q1^T q3' = 0? Does your q3' satisfy q2^T q3' = 0? Is your q3^T q3 = 1 ? ... Results will be posted on the net. EXTRA credit: When you have found the final Q and R matrices, do you see any reasonably simple formula for their coefficients?