Answered: Exercise 2: Given: vị = 3 , V2 = , V3 =… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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Question

Kindly solve both parts correctly and handwritten

Exercise 2: Given: v₁ =
·()--0--0--0--0
3 , = 0,03 = 2
, = 4,05 =
1
S₁ = {V₁, V₂), S₂ = {V3, V4}, S3 = {V₁, V2, V3), S4 = (v2, 04, 05), S5 = {V₁, V2, U3, U5), S6 = {U2, U3, U4, V5}
1. Which of S₁,..., S6 form bases to R³?
2. For the rest, find the dimension of span(S₂)
Exercise 3. In the vector space V - 2x2 define II JAG VI At 11 W
JACVI At
41
Look at the following sets:

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Enclosed by the cylinders z= x2 y = x 2 and the planes z =0 y =4
find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2
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Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. Find the general form of r(t), the position of the particle, as a function of time t, (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot).
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