Find a basis for the following plane in R3 1 + y - 2z = 0...

Question

Question

Answer 1

Answer #1

ut xty-220. put yes and zat . ut xty-220 put z=s and yet 20 25-t then in lyc2 M2=0 Uz=1 VIEL V2=1 4320

Answer 2

Similar Homework Help Questions

Find an ONB (orthonormal basis) for the following plane in R3 2 + y + 3z...

Find an ONB (orthonormal basis) for the following plane in R3 2 + y + 3z = 0 First, solve the system, then assign parameters s and t to the free variables (in this order), and write the solution in vector form as su + tv. Now normalize u to have norm 1 and call it ū. Then find the component of v orthogonal to the line spanned by u and normalize it, call it ū. Below, enter the components...
A plane in R3 is represented parametrically by the equation * = w + su +...

A plane in R3 is represented parametrically by the equation * = w + su + tv, where w= (139,0,0), -- (- 3:1, 0), and v = (5, 0, 1). Represent this plane in the form a1x1 + a2x2 + a3x3 = b, where x = (X1, X2, X3).
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2...

Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...

#12 6.3.20 s Question Help 5 0 Let un 2. u2 -8 and uz = 1...

#12 6.3.20 s Question Help 5 0 Let un 2. u2 -8 and uz = 1 Note that u, and uz are orthogonal. It can be shown that ug is not in the subspace W spanned by u, and up. Use this to - 1 0 construct a nonzero vector v in R3 that is orthogonal to u, and up. 4 The nonzero vector v = is orthogonal to u, and u2
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0},...

1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0}, where w.v is the dot product. 2 (a) Prove that U is a subspace of R3. (b) Find a basis for U and compute its dimension. 4. Decide whether or not the following subsets of vector spaces are linearly independent. If they are, prove it. If they aren't, write one as a linear combination of the others. (a) The subset {0 0 0 of...
(1 point) Find an orthonormal basis of the plane X1 + 4x2 – x3 = 0....

(1 point) Find an orthonormal basis of the plane X1 + 4x2 – x3 = 0. Answer: To enter a basis into WebWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 2 then you would enter [1,2,3], 3 [1,1,1) into the answer blank.

1. For each of the following statements, declare whether the statement is true or false, (a)...

1. For each of the following statements, declare whether the statement is true or false, (a) A system of four linear equations in three unknowns cannot have a solution. (b) 3.x + 3y - 2z = 0 is the equation of a plane through the origin in R', with normal vector (3,3. -2) (c) It is possible to determine if two lines in R3 intersect by solving an appropriate system of linear equations. (a) Find the parametric equation of the...
Please attempt both questions. 5. Find an orthonormal basis for the plane viewed as a subspace...

Please attempt both questions. 5. Find an orthonormal basis for the plane viewed as a subspace of R3. Z (-1,0,2) (0,-1,0) (0,1,0) X 6. Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): 1 2 5 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = 22 - 3, 9() = 4, h(x) = 2² +2}...
1. Consider the following Linear transformation L : R5 + R5 represented in the standard basis...

1. Consider the following Linear transformation L : R5 + R5 represented in the standard basis via the following matrix: 1 7 4 1 A= 2 4 6 9 -4 0 3 4 3 3 6 12 0 1 9 8 7 9 -2 0 2 (a) Find a basis for Null(A), Col(A), and Row(A). (b) For each v in your basis for Col(A) find a vector u ER5 do that Au = v. (c) Show that the vectors you...

6. Given the vectors vi = - 0 -- --(2.).-) no estaba 1. vz = 2...

6. Given the vectors vi = - 0 -- --(2.).-) no estaba 1. vz = 2 .03 = 1 -1 1 62-5) ,0 = 3, find the value(s) of k so that: de (a) vis in Span{vi, v2, U3}. (b){i, 03, 03} form a linearly independent set. (c){vi, už, va} form a basis for R3. (d) span{ti, uz, va} is a plane in R.