Solutions to ExercisesCollege of the RedwoodsMathematics DepartmentMath 45—Linear AlgebraQuiz #1—Linear AlgebraDavid ArnoldCopyrightc 2000 [email protected] Revision Date: October 10, 2001 Version 1.002Exercise 1. Show (geometrically) how vector b can be written as alinear combination of vectors u and v.uvb3Exercise 2. Write the system2x +3y − z =0x +2y + z =4y − 2z =2as a matrix equation.Exercise 3. Multiply.(a)2 −23112=(b)123456=Exercise 4. What 2 × 2 matrix reflects every vector in the planeacross the line y = x?4Exercise 5. What is the matrix A that is created by the followingMatlab commands?>> x=(1:2:5)’>> A=[x,x.^2,x.^3]Solutions to E xercises 5Solutions to ExercisesExercise 1. Using the parallelogram method for adding vectors, notethatb = αu + βv.uvbαuβvExercise 1Solutions to Exercises 6Exercise 2.23−112 101−2xyz=042Exercise 2Solutions to Exercises 7Exercise 3(a)2 −23112=2 −23112=−25Solutions to Exercises 8Exercise 3(b)123456=412351236123=4568101212 15 18Solutions to Exercises 9Exercise 4. The vector (x, y) is reflected across the line y = x ontothe vector (x, y).xyy = x(x, y)(y, x)Note that0110xy=yx.Exercise 4Solutions to Exercises 10Exercise 5.>> X=(1:2:5)’X=135>> A=[X, X.^2, X.^3]A=11139275 25 125Exercise
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