(3) For each of the matrices below: . Calculate the determinant and describe what it means as far as how the matrix would impact vector space as a transform. . If the matrix has an inverse, compute it. . If the matrix does not have an inverse, provide a clear reason why no such inverse could exist. O (a) A= 0 for some r, y E R where a * 0 and y / 0. 6 (b) B = (c) C = OH(4) The following scatter plot and table represent a random sample of ve students from our CS 2810 class and their age in months {scaled} and number of pets owned {scaled}. We will try to predict number of pets (3;) with age {at}. pet_sca|s 0 0 0.5 1.0 1 5 -0 .5 -1.0 -1.5 _ll||lll_ 1.5 -1_0 -0.5 0.0 0.5 1.0 1.5 age_scale student0 student 1 st udent2 st udent3 st udent4 age (scaled) | ~02 ~0.9 0.9 1.2 | 0.9 pet (scaled) | 0.5 0.5 -1.0 0.5 | 1.5 For all your answers below, please round to 2 decimal places of precision. Please also show all work, as necessary. (:1) Calculate the line of best t that has both a slope and intercept, i.e. of the form 3; = b + mm. (b) Calculate the line of best t that has a slope but passes through the origin, i.e. of the form 3; = min. Homework Assignment #5 4 (c) Calculate the line of best t that has only an intercept but no slope, i.e. of the form y = b. a Note: we didn't do this in class, but it should be relatively intuitive to gure out. (d) Calculate the line of best t that is a quadratic curve through the points, i.e. of the form 3,: = b+mlrr+m2m2 0 Note: To do this, you will need to set up the correct X matrix, and will need the inverse of X TX , which is provided {in rounded form) below: 1 .2 1 {XTX)l= .2 .3 .3 1 .3 1.3 (e) Use the plot on the previous page (or sketch your own) which shows each line/\"curve above overlaid on top of the scatter {use colored pencils, or different patterned lines (dashed, dotted, etc.) to differentiate the ts, make sure they are clearly labeled). Then, in a sentence or two, explain which t you think is best suited for describing the relationship between age and pet ownership based on these data