. Let A =     −2 −1 −1 2 1 0 0 2 5 3 0 3     . (a) Enter A into MATLAB and use MATLAB to compute the dot product of the first column of A with its second column. Also compute the dot product of the third column with itself. (See guide for how to extract a column from a matrix.) (b) Compute the matrix product AT A. (c) ? What is the relationship between the entries of AT A and the dot products of the columns of A? Make sure your answer is consistent with your computations. (d) ? What in general is the relationship between the entries of AAT and dot products of vectors associated to A? (e) Compute AAT and do at least two dot product computations to support your previous answer. (f) Let Q =   1/ √ 14 1/ √ 3 5/ √ 42 2/ √ 14 1/ √ 3 −4/ √ 42 3/ √ 14 −1/ √ 3 1/ √ 42  . Do a single matrix computation which shows that the columns of form an orthonormal set. (g) ? Explain carefully why your computation above shows that the columns form an orthonormal set. (h) ? Explain why the rows of Q must also form an orthonormal set.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.

What is the expression in factored form? -x^2 + 3x + 28 a. (x-7)(x-4) b. -(x-7)(x+4) c. (x+4)(x+7) d. -(x-4)(x+7)

Rounded to the nearest tenth, what is the value of x