Concept explainers
Additional Problems
Prove that if
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.arrow_forwardUse a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forwardLet S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from R3 into R3 such that the set {T(v1),T(v2),T(v3)} is linearly dependent.arrow_forward
- Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises 22-31 are linearly independent. If, for any of these, the answer can be determined by inspection (i.e., without calculation), state why. For any sets that are linearly dependent, find a dependence relationship among the vectors. [1121],[3224],[2311]arrow_forwardLet u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.arrow_forwardTake this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)arrow_forward
- For which values of t is each set linearly independent? a S={(t,1,1),(1,t,1),(1,1,t)} b S={(t,1,1),(1,0,1),(1,1,3t)}arrow_forward3. Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4. -7, 1, 3) form a linearly dependent set in R*? 4. Express V1 in number 3 as linear combination of V2 and V3. %3Darrow_forward10. (a) The non-zero vectors a, b andc are such that axb exa. Given that b -e, find a linear relationship between a, b and c. (b) The variable vector v satisfies the equation vx(i-3k)= 2j. Find the set of vectors v and [(b) v = HER] fully describe this set geometrically.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage