An orthogonal basis for A, 10 2 - 6 16 2 with the given orthogonal basis. - 2 4 0 10 10 16 -148 -4 16 22 22 10 10 -4 The QR factorization of A is A = QR, where Q = is and R= 10 2 -6 16 2 4 4 -4 0 4 6 0 6 SO 0 0 5 0 O -5 Find the QR factorization of A

Please show me how to answer in excel. Questions 3-6.

Solve each equation for 0<0 < 2n. 9) -3 + 2tan 20 = -3 10) 5- 2cos 20 = 6 12) -3 - csc 30 =-2 11) 2- 3sec =-4

Consider the DE d²y dy dx² which is linear with constant coefficients. 8 + 16y = x dx First we will work on solving the corresponding homogeneous equation. The auxiliary equation (using m as your variable) is = 0 which has root Because this is a repeated root, we don't have much choice but to use the exponential function corresponding to this root: reduction of order. Y2 = ue4x Then (using the prime notation for the derivatives) Y/₂ Y So, plugging y2 into the left side of the differential equation, and reducing, we get y2-8y2 + 16y2 = U = So now our equation is e4u" = x. To solve for u we need only integrate ce-4 twice, using a as our first constant of integration and b as the second we get Therefore y2 = general solution. to do the We knew from the beginning that e4 was a solution. We have worked out is that xe4 is another solution to the homogeneous equation, which is generally the case when we have multiple roots. Then 2+4 is the particular 64 solution to the nonhomogeneous…