PROBLEMS
For Problems 1-14, determine the component
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
- 1. Write the vector H- 16 as a linear combination of the vectors and Darrow_forward1. Let x = i +4j + 2k and y = i-3j - k. In this question, write all vectors in i, j, k notation. (a) ( Find |x||. (b) M Find 2x + 3y. (c) Find x. y. (d) Find x × y. Answer: Answer: Answer:arrow_forwardFind (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_forward
- For the following problems, you need to provide a clear and detailed solution. Work Problem1 1 (a) [. - | Determine if the vectors 0 and| 1 span R³. -2 3 (b;. -- ] Can these three vectors form a basis for R'.arrow_forwardA B -1 -2 C D E -4 -5 -3 F 1 GHI 2 3 L JK -1 -2 4 5 P Q R 2 3 1 MNO -5 -4 -3 TU S 4 5 -1 V -2 W X -3 -4 Y 1 N 2 Use the table above to create two vectors in 2-Space: * and y Let * be a vector representative of the first two letters in your given name and y represent the first two letters of your surname. (Ex. Albert Einstein: x= [-1, -2] and y = [-5,4]) My vectors are 2 = [-1₁-4] and j = [ -5, -2] Use the table above to create two vectors in 3-Space: è and f Let è be a vector representative of the first three letters in your given name and represent the first three letters of your surname. (Ex. Albert Einstein: € = [-1, -2, -2] and f = [-5,4,-4]) My vectors are è = [-1,-4, 2] and f= [-5, -2₁ -2] e 1. Angle Between Vectors and Projects a) Use the dot product to verify the type of angle connecting the vectors and y (acute, right or obtuse). b) Find the angle connecting the vectors and y in two different ways. c) Use the dot product to verify the type of angle connecting the vectors e and…arrow_forwardGiven a the vector equation r(t)=(3+4t)i+(−2+3t)j+(−3+1t)kr(t)=(3+4t)i+(−2+3t)j+(−3+1t)k, rewrite this in terms of the symmetric equations for the line. (quotient involving x) (quotient involving y) = (quotient involving z) =arrow_forward
- Need help with these vector problems pleasearrow_forward[1 1 1 -1 Let u1 = u2 Uz = then write x as sum of two vectors -3 3 on in span {u} and other one in span {u2, U3,} -2 2 x = 3 -3 (a) X = (b) 3 2 0. 3 [1 (d) 1 X = 3 -3 4. + +arrow_forwardIf v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.arrow_forward
- So, how would I find the vector of 3v in this problem?arrow_forwardThe following question is from linear algebra : Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step.arrow_forward[3] 1. Show whether the vector w = |1 is in span2 [5] 2. Show whether the following polynomial vectors are linearly independent or dependent. P1 = 1+ x, P2 = 1+ 2x², P3 = 2x + 3x²arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education