All questions except question 3

Start Maple and load the linear algebra library: with(Linear Algebra); We will start this week with two questions from last week's test: Define > T1:=Matrix(3,4,[[1,1,-1,5),(1,2,1,3],[1,1,d^2-26,d]]); Use > T2:=Pivot(T1,1,1); Note the third row can contain three zeros on the left of the dotted line for d equal to +5 or -5. Q1a Set to be equal to each of these in turn in Tla and Tib respectively > Tia:=Matrix(3,4,[[1,1,-1,5],[1,2,1,3],[1,1,-1,5]]); > Tib:=Matrix(3,4.[[1,1,-1,5],[1,2,1,3],[1,1,-1,-5]]); Use > ReducedRowEchelonForm(Tia); > ReducedRowEchelonForm(T1b); for both new matrices and identify and check all solutions for both cases in the original equations. [2 marks] Q1b Based on T2, pick a different value for d which will give an integer solution for 2 and verify that its solutions for x and y will also then be integers. [1 mark] Q2a Set > vt :=; Show that x = -1, y = 3, 2 = 2 and W 2-5 is of this form by evaluating > subs({s=3,t=-5},vt); Now set > vh!-(-5,5,-t,t>; Check similarly if x = -2, y = 2, 2 = -1, W = 1 or x = 1, y = 1, 2 = -2, W = 2 are of the form of vt or vh. [2 marks] Q3 For the next test, we want you to create a single pdf file with all of your work in which you will then send to Dr. Mitra, not through Moodle! One way to do this is using Microsoft Word. You all have access to this through CBU: https://www.cbu.ca/future-students/student-services/it-services/office-365/ Please install Word if haven't already got it and open a blank document. You can now drag and drop image files into this document and then go to File/Export and Create PDF/XPS from that. Select PDF and Publish to create your pdf. For this lab, please add TWO images of your scrap work and create a PDF file of them. If you have another method to do this, that is also fine. Name the file with lab4, hyphen and YOUR & digit registration number, so for instance the name could be lab4-12345678.pdf Upload this file to Teams along with your .mw file at the end of the lab for the marks. [2 marks] Define these two matrices: > Am!=|>; > Bm;=||>; 04a Note what Maple's response is when you try to add them using: > Cm: Am Bm Now evaluate > Dm: Am+Transpose(Bm); and > Em: -1/2Dm; Explain using #why these results are as you would expect. [1 mark) 046 Maple can calculate the Rank of a matrix directly. > Rank (Am): > Rank (Em) :| Create a matrix Fm such that > Rank (Am+Fm): is 1. What is the Rank of Fm? Now create Gm such that > Rank (Am+Gm); is also 1 but Rank (Gm) is not the same as Rank (Fm) [2 marks] Start Maple and load the linear algebra library: with(Linear Algebra); We will start this week with two questions from last week's test: Define > T1:=Matrix(3,4,[[1,1,-1,5),(1,2,1,3],[1,1,d^2-26,d]]); Use > T2:=Pivot(T1,1,1); Note the third row can contain three zeros on the left of the dotted line for d equal to +5 or -5. Q1a Set to be equal to each of these in turn in Tla and Tib respectively > Tia:=Matrix(3,4,[[1,1,-1,5],[1,2,1,3],[1,1,-1,5]]); > Tib:=Matrix(3,4.[[1,1,-1,5],[1,2,1,3],[1,1,-1,-5]]); Use > ReducedRowEchelonForm(Tia); > ReducedRowEchelonForm(T1b); for both new matrices and identify and check all solutions for both cases in the original equations. [2 marks] Q1b Based on T2, pick a different value for d which will give an integer solution for 2 and verify that its solutions for x and y will also then be integers. [1 mark] Q2a Set > vt :=; Show that x = -1, y = 3, 2 = 2 and W 2-5 is of this form by evaluating > subs({s=3,t=-5},vt); Now set > vh!-(-5,5,-t,t>; Check similarly if x = -2, y = 2, 2 = -1, W = 1 or x = 1, y = 1, 2 = -2, W = 2 are of the form of vt or vh. [2 marks] Q3 For the next test, we want you to create a single pdf file with all of your work in which you will then send to Dr. Mitra, not through Moodle! One way to do this is using Microsoft Word. You all have access to this through CBU: https://www.cbu.ca/future-students/student-services/it-services/office-365/ Please install Word if haven't already got it and open a blank document. You can now drag and drop image files into this document and then go to File/Export and Create PDF/XPS from that. Select PDF and Publish to create your pdf. For this lab, please add TWO images of your scrap work and create a PDF file of them. If you have another method to do this, that is also fine. Name the file with lab4, hyphen and YOUR & digit registration number, so for instance the name could be lab4-12345678.pdf Upload this file to Teams along with your .mw file at the end of the lab for the marks. [2 marks] Define these two matrices: > Am!=|>; > Bm;=||>; 04a Note what Maple's response is when you try to add them using: > Cm: Am Bm Now evaluate > Dm: Am+Transpose(Bm); and > Em: -1/2Dm; Explain using #why these results are as you would expect. [1 mark) 046 Maple can calculate the Rank of a matrix directly. > Rank (Am): > Rank (Em) :| Create a matrix Fm such that > Rank (Am+Fm): is 1. What is the Rank of Fm? Now create Gm such that > Rank (Am+Gm); is also 1 but Rank (Gm) is not the same as Rank (Fm) [2 marks]