Problems
For Problems 1-5, determine whether the given set of
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Differential Equations and Linear Algebra (4th Edition)
- 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .arrow_forwardFor each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two. (a) (-2,0,3) ,(1,3,0),(2,4,-1) (b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1) (c) (3,4,1) ,(1,-2,1), (-2,-1,1) (d) (2,-1,0) , (1,2,-3), (1,-3,2) (e) (5,1,-5) , (1,-2,-3), (-2,3,-4) (f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)arrow_forward1. Find all solutions: 2. In what ways can 88-8 and be written x+y ==0 a as a linear combination of [] [] [4], and ² 3. Show that the vector 2 is NOT contained in the span of the following three vectors 6 4. For which b are the vectors -0.0 x+2y+z=5 2x+3y-z=3 independent?arrow_forward
- Find (a) v x w, (b) w x v, and (c) v x v for the two given vectors. v = j + k, w = 2i +2j +3 k (a) v x w = ai +bj +ck where O. b=. and c= (Type exact values, in simplified form, using fractions and radicals as needed. Type 1, -1, or 0 when appropriate, even though these valu usually shown explicitly when writing a vector in terms of its components.) (b) w x v = ai +bj +ck where , b=. and c= (Type exact values, in simplified form, using fractions and radicals as needed. Type 1, - 1, or 0 when appropriate, even though these values usually shown explicitly when writing a vector in terms of its components.)arrow_forwardA = ( ) -3. Find a non-zero number 1 and a non-zero vector x so that Ax = 1x. Note: There are only two possible values for 2. You just need to find one of them. For each 1 there are lots of vectors i. You just need to find a non-zero one. To get full credit, you must find your values systematically rather than guessing. Guess and check will receive partial credit.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning