11. In the vector space R3 we are given the subspace Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > . (a) Which conditions must the real numbers a, b and c satisfy in order the vector (a, b, c) lies in the subspace Y ? (b) Find a basis for Y. (c) Extend the basis you have found in (b) to a basis of the whole space R3.

11. In the vector space R3 we are given the subspace Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > . (a) Which conditions must the real numbers a, b and c satisfy in order the vector (a, b, c) lies in the subspace Y ? (b) Find a basis for Y. (c) Extend the basis you have found in (b) to a basis of the whole space R3.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b –…

A: The solution is given as

Q: Let v₁ = -8--8 V2 Basis = (a) Convert (v1, v2} into an orhonormal basis of W NOTE: If your answer…

Q: In the vector space R the vectors a = (1,0,0,-1), 5= (1,0,1,2), y = (1,0, 8, 1) are given. (a) Is…

Q: The vector x is in a subspace H with a basis ß = {b1,b2}. Find the ß-coordinate vector of x. b₁ =…

Q: 11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a +…

A: To find: Basis of W={(a,b,c,d) | a+b-c+d=0}.

Q: The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. - 2 4H9…

Q: - (-, s) Find a basis for the subspace W C R', consisting of all the vectors orthogonal to the…

Q: Let W be a subspace of R4 spanned by the set Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}. (i)…

Q: 8) Find a basis for the space spanned by the 5 vectors listed below O T 1 2 26 4 1-1, 1, 0, 1 3…

A: Concept: Reduced roe echelon form abbreviation is (rref) When a matrix is in row echelon form,…

Q: i) Determine the linear mapping T : R3 → R² which maps the basis vectors {(1,0,0), (0, 1,0), (0,0,…

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: b Ell С pts] Explain how you know that W is a subspace of R¹. er W = a+b+5c = 0, b+2c=0, a +3c+d=0

Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: s) Determine if these vectors for a basis for R³: linear combination of these vectors. 0·0-0--0- and…

Q: For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. p-8q 4p + 2r…

Q: Find a basis for the subspace of R° that is spanned by the vectors V1= (1,0,0), v2 = (1, 0, 1), v3 =…

Q: Find the general solution for y' = x – 4xy using an integrating factor.

Q: 6. Let V = R³ and F = R. Let W = { (a, b, c) | a+b-2c=0 where a, b, c are in R} It can be shown that…

Q: - {{:) ()(}} (3) 2 B be an ordered basis of the vector space R³. Let the vector v = Find the…

Q: Consider the following vectors! x₁ = x2= 6 x3 =1 16 -5 X=[²] { Ⓒ) are the weckers S [ X₁, X₁, X3z…

Q: 2. Consider vectors of the form 2y + 5y 4y 3x + + 5z] 2х 8z ,x, y,z are real # - W = -x + 7z y +…

A: Solve the following

Q: X1 ER* satisfying the X3 X2 6. Show that the set of all vectors XA equations 3x1 - 2x2- X3-4x4 = 0…

Q: #6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of…

Q: Let W be a subspace of Rº generated by the following vectors 1 1 2 1 2 W1 W2 W3 W4 = W5 8. -2 3 8 a:…

Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: Put I, in equ (1) 80 = 61 + 6( 1² + 1) 12 3 -- I = 7amp.

Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

Q: ii) Two subspaces of R3 are U = {(x,y, z) : x – 3y – 2z = 0} and W = %3D {(r, y, z) : x – y = 0}.…

Q: Find a basis for the subspace of R° spanned by the following vectors. 6. 18 -3 -3 6 6. -18 -18 14…

A: We solve this by row reduced echolon form

Q: (a) Find orthonormal vectors 91, 92, 93 such that 91, 92 span the column space of 1 2 1 A - 1 -2 4…

Q: Determine a basis for the subspace of R that consists of vectors the form (a, b, c, a - 5b + 4c).…

Q: In each item, you are given a set of vectors S the vectors into the columns of a matrix A rref R of…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: 4. Find a basis of each vector space below and hence write down the dimension of the space. You do…

A: We have been given 4 vector spaces and we need to determine the Basis in each case.

Q: Which of the following subsets of R 3 are actually subspaces?(a) The plane of vectors (b1, b2, b3 )…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Q 3: a) i. Show that W is a subspace of R*. ii. Find a basis for W. Let W = ((a +c, a + b + 2c, a +…

A: According to the policy we are allowed to do only one question with their sub-parts (If any). So I…

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, 0),…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

11. In the vector space R3 we are given the subspace
Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > .
(a) Which conditions must the real numbers a, b and c satisfy in order
the vector (a, b, c) lies in the subspace Y ?
(b) Find a basis for Y.
(c) Extend the basis you have found in (b) to a basis of the whole space
R3.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Pls solve this question correctly instantly in 5 min i will give u 3 like for sure
Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a + 7b and d = a- 6b. (A) {(1, 0, 1, 1), (0, 1, 7, —6)}; (В) {(0, 1, 7, 1), (0, 1, 1, —6)} (С) {(1, 1, 0, 1), (1, 0, 7, —6)} (D) {(0, 1, 7, 1), (1, 1, 0, –6)} (E) {(1, 0, 7, 1), (0, 1, 1, –6)} (F) {(1, 1, 0, 1), (0, 1, 7, –6)} (G) {(1, 0, 1, 1), (1, 0, 7, —6)} (Н) {(1, 0, 7, 1), (1, 0, 1, —6)}
Spent a lot of time solving it, need some help
If V is the subspace spanned by (1, 1, 0, 1) and (0, 0, 1, 0), find (a) a basis for the orthogonal complement V-L. (b) the projection matrix P onto V. (c) the vector in V closest to the vector b = (0, 1, 0, -1) in V¹.
(a) Every vector of R² is a linear combination of the vectors (-2,3), (1, 1) and (4,1)? (b) Is every vector in R³a linear combination of the vectors (-2, 1, 3) and (3, 2, 1)? (c) The Vector (2, –1,2) belong to the subspace generated by vectors (3,2, -1) and (-3,0,2}?
Find a basis for the orthogonal complement of the subspace of Rª spanned by the following vectors. V1 = (1,-1,7,3), V2 = (2,-1,5,2), V3 = (1, 0, -2, -1) The required basis can be written in the form {(x, y, 1, 0), (z, w, 0, 1)}.
How do I work this problem out?
could you please help me with all parts
9 Find a basis and the dimension for the vector subspace W = ((x,y,z) e R³/ 2x-y+2=0 -8x+4y-4z=0} -6x+3y-3z0
*1. Let W be the subspace of R5 spanned by the vectors B Find a basis for W. Give the dimension of W. -3 b₁ = 2 *2. Consider B = {b₁,b₂}, a basis for R² where - (²). b₂ = (3) 0 (a) Find the change of basis matrix that converts vectors given with respect to B into vectors given with respect to the standard basis. Give your matrix explicitly. (b) Find the change of basis matrix that converts vectors given with respect to the standard basis into vectors given with respect to B. Give your matrix explicitly. 3. True or False? (a) There is a 5 x 3 matrix whose column space is 1-dimensional. (b) If A is an m x n matrix, then rank(A) + nullity(A) = m. (c) If A is an n x n matrix and the columns of A span R", then A is invertible. (d) If B is a 2 x 2 matrix and B² = I₂, then B = I2. (e) The kernel of the function T: R² R² given by T + (²) - (² + 1) ₁ = is {0}. (f) There is a matrix that has a 3-dimensional column space and a 2-dimensional row space.
4. Vector u is a unit vector orthogonal to vectors a and b, where a = i+j-k, b=2i-j. Then the coordinates of vector u in the basis {i, j,k} are 2 3 (a) (b) (-1, 2,–3) (c) None of the above is true
Let fi = 1+2x + 3x², f2 = 2 + 3x + 4x². B = (f1, f2) is a basis for the subspace V = {ao +a1x+azx²[ao – 2a1 +a2 = 0} of R2[r]. Let g = 1+5x + 9x². If [g]g = (,) then s = a) -7 b) -5 c) 5 d) 7 e) g is not in V.