Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
luck
Group Title
determine bases for the following subspaces of R^3 a) the plane 3x2y+5z
 3 years ago
 3 years ago
luck Group Title
determine bases for the following subspaces of R^3 a) the plane 3x2y+5z
 3 years ago
 3 years ago

This Question is Closed

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Thank you, luck :^)
 3 years ago

luck Group TitleBest ResponseYou've already chosen the best response.0
sir its my pleasure that you are helping me
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
That plane 3x  2y + 5x = 0 is a two dimensional subapace of \[\mathbb{R}^{3} .\] If we solve for z in terms of x and y, we get z = (3x + 2y)/5. Letting x = 1, y = 0 makes z = 3/5. Letting x = 0, y = 1 makes z = 2/5, so two linearly independent vectors in the subspace are [1,0,3/5] and [0,1, 2/5]. Those two vectors form a basis for the subspace \[B = \left\{ [x, y, z]3x  2y + 5z = 0 \right\}.\]
 3 years ago

luck Group TitleBest ResponseYou've already chosen the best response.0
Consider the operation on p2 that takes ax^2+bx+c to cx^2+bx+a . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix? (b) Consider the operation on p3 that takesax^3+bx^2+cx+d to cx^3bx^2ax+d . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix?
 3 years ago

luck Group TitleBest ResponseYou've already chosen the best response.0
can you solve above question
 3 years ago

oswaldo669 Group TitleBest ResponseYou've already chosen the best response.0
Someone help on my problems.
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Let us consider n, a unit normal vector to the plane at the origin, and \[u_1 ,\] the unit vector in the direction of [1, 0 ,3/5]. \[n = [3, 2, 5]/\sqrt{3^{2} + (2)^{2} + 5^{2},}\] \[u_1 = [5/\sqrt{34}, 0 3/\sqrt{34}].\] If we take the cross product of unit normal vector N with \[u_1 ,\]we get another unit vector \[u_2\]in the subspace S, so those two vectors form another basis if S; in fact, it is an orthonormal basis of S. To determine what \[u_2\]is, evaluate the determinant of matrix [[ i, j, k ], [3/sqrt(38), 2/sqrt(38), 5/sqrt(38)], [5/sqrt(34), 0, 3/sqrt(34)]] = [6/sqrt(1292), 34/sqrt(1292), 10/sqrt(1292)], simplifying to [3/ sqrt(323), 17/sqrt(323), 5/sqrt(323) ]. Thus, an orthonormal basis for subspace S is\[\left\{ u_1, u_2 \right\},\]where \[u_1 = [5/\sqrt{34}, 0, 3/\sqrt{34}],\] \[u_2 = [3/\sqrt{323}, 17/\sqrt{323}, 5/\sqrt{323}].\]
 3 years ago

luck Group TitleBest ResponseYou've already chosen the best response.0
solve this please (b) Consider the operation on p3 that takes ax^3+bx^2+cx+d to cx^3bx^2ax+d . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix?
 3 years ago

DevinBlade Group TitleBest ResponseYou've already chosen the best response.3
luck you should be asking one question at a time as a new one so he can get more medals for such awesome answers ;D
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Thank you, luck :^)
 3 years ago

luck Group TitleBest ResponseYou've already chosen the best response.0
sir can you solve the question i posted recently
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Let me see can I find it...
 3 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.