PROBLEMS
For Problems 1-14, determine the component
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EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- A 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_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_forwardEscalatearrow_forward
- Problem 2: Assume that M and N are non-zero vectors. Using properties of vectors, explain why M · (M × N) = 0. (Note: there are multiple ways to answer this question. Also, you should NOT be using component form here).arrow_forwardProblem 6. Suppose that V₁, V2 and v3 are linearly independent vectors in a vector space V. Prove that the vectors W₁ = V₁ + V2, W2 = V₂ + V3 and w3 = V3 + V₁ are also linearly independent in V.arrow_forwardPlease solve first 4 partarrow_forward
- 2. Given a = 5e2 and b = 2e₁ + €3, let C = ab. If the tensor C operates on another vector d = 7e₁ +2e2- €3: (a) Calculate the resulting vector. (b) Symbolically, how would the result be expressed in terms of b, d and a?arrow_forward3. The vectors Y and w have their bases. at the origin, (0,0), and hence may be fully. described by the Coordinates of their heads which we designate as B and B', respectively. In each problem find (a) xtw, (b) x-w, and (c) 3y-4w B= (6,2), B'=(1,2)arrow_forwardProblem #9: Given three linearly independent vectors V₁ = (-9,3,-9,9,-2), V2 = (-8, 10, 9, -3, 10), V3 = (-7,-9,-7, -7,0), in R5, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e, and ej then enter the values of i and j into the answer box below, separated with a comma. Problem #9:arrow_forward
- -2 2 if a = 3 b = 4 Represent each of the following as a single column vector:, Draw vector diagrams a 2a b 3b C 2b – a d (a - b) e 2a – 3c f 3c- aarrow_forwardIf u = < 3 , 9 > and v = < -3, 1 >, find 1/3u - 2v. (this is a vector problem)arrow_forwardProblem #9: Given three linearly independent vectors V₁ = (-9,3,-9,9,-2), V2 = (-8, 10, 9, -3, 10), V3 = (-7,-9,-7, -7,0), in RS, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e, and e; then enter the values of i and j into the answer box below, separated with a comma. Problem #9:arrow_forward
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