Question

Given the data (t1, b) = (-1,-4) (t2, b2) = (0,2) (t3, 63) = (1,2) (t4,64) = (2, -7), find the linear equation f(t) = cit+co that best fits f(ti) = bị. a.(5 points) Find the matrix A for which you can rephrase the problem as solving Ax* 2 2 -7 7 C1 for which x* = [e gives the least-square solution. Со b.(15 points) Solve the least-square problem and find cit+ Co.

Answer 1

solha) me pare dhe linear equation #lt)= (t +co briven data prints: (-)-42, (0,2), (1,2), ( 2-1) Put the rames of to and f(t) from these we get data points -4 = (-1 to 2 = (otco CCD+co -7 = C, (2) to a 25 (ic, to=-4 0.c, tco = 2 1.c, & co =2 2.9, + (0 = -7 witte hul linear equation in matty A = b youm fam: -4 2 0 CO 2 2 -7 the malety Aů A= O - - 2 b) for least-squares solution, we need to some (ATA)'' (Ab)

Now ΑΤΑ. 17 0 1 2 - 0 6 2. - 4 2 1 - 1 1 - 1 KATA 6 2 4 -2 1 20 Vs Yo -Yo 3/10 2 ५ -26 LATb I-lo 7 2 2 1 - -1 - 2 ។ * - -710 15 1-%0 -1/10 3/10 11 1-7 L-13/10 we get a 0.9 10 -13 = -T3 10 Co = then, f(t)= -0.9t -113