Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0} be a subspaceof P3. Then the dimension of W is equal toO 4O 2O None of these

Answered: Let W = {a + bx+ cx² + dx³| a + b = 0,c…

Let W = {a + bx+ cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0} be a subspace of Pg. Then the dimension of W is equal to %3! O 4 O 2 O None of these

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 42EQ

See similar textbooks

Related questions

Q: Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.

Q: Let S E M2x2; a = d and b +c = 0} be a subspace of Max2. %3D Then the dimension of S is equal to: O…

Q: Show that the solution set to a system of equations of the form a + a, x = 0 + an x = 0 a m, + ... +…

Q: Consider the subspace V of R4 given by 1 3 1 V = span || -1 1 1

A: Solution:-

Q: find a basis for the given subspace of R3, and state its dimension. All vectors of the form (a, b,…

Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find The closest point y in the subspace W spanned by v1 and v2.

Q: Let W = {a + bx + cx? + dx³| a + b = 0 and c – 3d = 0} be a subspace of P3. Then the dimension of W…

Q: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

Q: Let S = E M2x2; a = d and b +c = 0} be a subspace of M2x2- Then the dimension of S is equal to: 1 4

A: S=abcd∈M2×2; a=d and b+c=0 be a subspace of M2×2

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

Q: 4. Use the definition of a subspace to prove that the set V:= :, y, z E R, y+ : 0 is a subspace of…

Q: Let W = {a + bx + cx? + dx³| a + b 0,c-a = 0, and d-3a = 0} be a subspace of P. Then the dimension…

A: We have to choose the correct answer from the given options

Q: Let B a 3x3 square matrix, and let λ be a scalar. a) Prove that the set K = { x | Ax = λx} is a…

A: Subspace : Let V be a vector space over a field F and W a subset of V. Then W is a subspace of V if…

Q: Show that H= {p € P3: p(0)+p(1) = 0} is a subspace of P3. %3D

Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

Q: Let W {a + bx + cx2 + dx³| a + b = 0 and c - 3d = 0} be a subspace of P3. %3D Then the dimension of…

Q: Find a basis for the subspace and state the dimension. {[ 2c a − b b − 3c a + 2b ]:a, b, c in R}.

A: The given subspace is 2ca-bb-3ca+2b. 2ca-bb-3ca+2b=a0101+b0-112+c20-30 Note that, the vectors…

Q: 4. Let A be a real m x n matrix. Show that U = {x E R" : Ax = 0} is a subspace of R".

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Let W = {a + bx + cx² + dx³| c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to

A: As given W be a subspace of P3.

Q: Let W = (a + bx+ cx + dx'|a+ b= 0 and c -3d = 0 ) be a subspace of P Then the dimension of W is…

Q: Let W = (a + bx + cx? + dx³la + 2c 0 andb-d D 0) be a subspace of P,. %3D Then dimension of W is…

A: Given W={a+bx+cx2+dx3| a+2c=0 and b-d=0}Since a+2c=0⇒a=-2cand b-d=0⇒b=dwhich gives…

Q: Let W = {a + bx + cx? +dx']c = a + b } be a subspace of P3. Then dimension of W is equal to: O 2 O 3…

A: To find the dimension of W.

Q: Theorem 6.14. For any a < b in R, the subspace [a, b] is compact.

A: The objective is to prove that any a≤b in ℝ the subspace a,b is compact. Let's prove the theorem by…

Q: If Sz is a subspace of R* of dimension 3, then there cannot exist a subspace S2 of R* such that S, c…

A: S1, S2 are subspaces of R4 such that S1⊂S2⊂R4 with S1≠S2 and S2≠R4.

Q: Let W = {a + bx + cx2 + dx'|c-3d = 0} be a subspace of P, Then the dimension of W is equal to %3D 4.…

Q: Let W = (a+ bx + cx² + dx*| a +b= 0,c-a = 0, and d-3a = 0) be a subspace of P. Then the dimension of…

A: The dimension of the vector space of polynomials in x with real coefficients having degree at most .

Q: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0 Let A=abcd, a,b,c,dER AT=acbd AT1-2=→0 ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

Q: Let W = {a + bx + cx? + dx³|c – 3d = 0} be a subspace of P3. Then the dimension of W is equal to…

Q: Consider the subspace W = {(a, b, c) E R³ : a – 26 – 3c = 0} of R³. (a) Is {(5, 1,1)} a linearly…

A: (a) Yes. The detailed explanation is as follows below:

Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

Q: Let W = {a + bx + cx2 + dx'| a + b = 0,c- a = 0, and d-3a = 0 } be a subspace of P. Then the…

A: 1 is the answer.

Q: Find a basis and the dimension of the subspace W of P3= {ax3+ bx2 + cx + d} defined by W = {PEP3:…

Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

Q: If W is a subspace of R" and ax is in W, where a is a nonzero scalar and x is in R". Then x is in W/…

A: We have to check

Q: 3). Determine whether the set of all matrices of the form a b c de f where a +c= 0, and b+d+ f = 0,…

Q: Let V = M22 and W = {invertible 2 x 2 matrices}. Determine whether W is a subspace of M2. %3D

Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

Q: Let S = {" E M2xzi a = d and b+c 0 be a subspace of M2x2. %3D Then the dimension of S is equal to: 4…

Q: An m×n matrix A is called upper triangular if all entries lying below the diagonal entries are zero,…

A: Proof:

Q: Let W = {a + bx + cx? + dx*Ia + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W…

A: Use the concept that dimension of subspace is number of free variables.

Q: Is the set M={1/n | n ε z+} compact as a subspace of R?

Q: Consider the subspaces U = span{[3 -3 1],[12 3 -7]} and W = span{[-3 2 0],[1 8 -6]} of V = R1x3.…

Q: Find all values of h such that y will be in the subspace of R³ spanned 3] by v1, V2, V3 if v1 =| 2|,…

Q: Let W = {a + bx + cx? + dx*| a + b 0,c-a = 0, and d- 3a = 0} be a subspace of P3. Then the dimension…

Q: Show that the solution set to a system of equations of the form au*, + Azyš, + + a, x = 0 Inn + ar =…

A: The given system of homogeneous linear equations is equivalent to a matrix equation of the form: Ax…

Q: Let H be the set of all vectors of the form (a – 3b, b - a, a, b) where a and b are arbitrary…

Q: Let W = {a + bx + cx2 + dx³| a +b = 0,c - a = 0, and d - 3a = 0} be a subspace of P3. Then the…

A: We have to check

Q: Let W = {a + bx + cx2 + dx³| a + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W…

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

Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0} be a subspace
of P3. Then the dimension of W is equal to
O 4
O 2
O None of these

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 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, algebra and related others by exploring similar questions and additional content below.

Similar questions

In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 37. V = P, W is the set of all polynomials of degree 3
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}
Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba+b+1]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set of diagonal nn matrices
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abcd]:adbc}
Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?