solve Determine whether the set of all matrices of the formb cwhere a +c = 0, and b+ d + f = 0,d eis a subspace of the vector space M2x3, of all 2 x 3 matrices.

Answered: Determine whether the set of all…

Determine whether the set of all matrices of the form (:: ;). a bc 1o), where a+e 0, and b +d+f 0, is a subspace of the vector space M2x3, of all 2 x 3 matrices.

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 31EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set...

See similar textbooks

Related questions

Q: (2) Find a basis for the subspace W = {(a +c, 2a – b, 3a – 26 – c,b+ 2c) | a, b, c € R} of R.

A: We need to find the basis for the given subspace:

Q: Determine whether each of the following is a subspace of the parent vector space. The set of…

A: To determine whether the given subsets are subspaces

Q: Find a basis for the subspace S of R4 consisting of all vectors of the form (a + b, a − b + 2c, b,…

A: We have to find the basis for the subspace S. We have to find the dimension of S.

Q: Find a basis for the subspace of R^4 that is spanned by the vectors v1 = (1, 1, 1, 1), v2 = (2,2, 2,…

A: Let us consider set S then the set S is linearly independent or dependent Determine the linear…

Q: Let W be the set of all 2 × 2 matrices A = " 2 га b] such that Az = 0, where z = . Is W subspace of…

A: A set W of vector space V over field F is said to be subspace of vector space V if W is itself a…

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

Q: let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given…

A: S forms a subspace of R2

Q: Determine whether the following are subspaces of R2×2: The set of all 2 × 2 matrices B such that b11…

Q: Show that if B is a basis for a subspace H, then each vector in H can be written in only one way as…

Q: let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given…

Q: In each part, find a basis for the given subspace of R4 .(2) All vectors of the form (a, b, c, d)…

Q: Verify that W is a subspace of V. In each case, assume that V has the standard operations.

Q: Find a basis for the subspace of P2 spanned by the given vectors. 1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

Q: Determine: If W = the set of all vectors in R2 whose second component is the square of the first. is…

Q: Is the set of all vectors of the formb, where a, b, and c are any real numbers with a +b+c > 0, a…

A: A subset W of Rn is a subspace of Rn if it satisfies Non-emptiness: The zero vector is in W.…

Q: Determine whether the following are subspaces of R2×2: The set of all 2 × 2 lower triangular…

Q: Find a basis and the dimension of the given subspace of R4: a + c a – b b+c E R4 -a + b

Q: Find a basis for the subspace а : a, b, c, d E R with 3a + b=0 and c+ d = 0 C W = 6. 6. d of R4.

A: Since 3a+b=0 Therefore b= -3a And since c+d=0 Therefore d= -c

Q: Show that H = : a, b eR is a subspace of M2x2(R). Hint: try to write H as the spa of a set of…

Q: Determine if W is a subspace of R³, and show why or why not

A: In this question, we have to check the given set is subspace or not

Q: Determine which of the following sets is a subspace of M2x2 (R). Select one: O a. U = {[* } O b. The…

A: To find the Subspace of M2×2(R).

Q: Let W be the subspace of all symmetric matrices in M2,2. What is the dimension of W?

Q: Determine whether the following are subspaces of R2×2: The set of all 2 × 2 matrices A such that a12…

Q: Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that…

Q: Let W be the set of all 3 x 3 matrices whose trace is zero. Show that S is a subspace of M33.

A: Let W be the set of all 3×3 matrices whose trace is zero. Show that W is a subspace of M33.

Q: Determine whether W is a subspace of V V = Mnn, W is the set of diagonal n X n matrices

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

Q: If W is a subspace of ℝ4 whose dimension is 2 then is any set of 2 vector is a basis for W

A: Answer

Q: Let B be a fixed mxn matrix and let S be the set of nxp matrices where S={A|BA=0}. Determine if S is…

Q: Consider the vector space M23 of all 2 × 3 matrices with the usual operations of matrix addition and…

A: To determine W is a subspace of M23 for that we have to check weather W is closes under addition and…

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

Q: Let 5 Find a basis of the subspace of R4 consisting of all vectors perpendicular to v.

Q: Show that the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the…

A: Given: the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the standard…

Q: Given two n xn matrices A and B, prove that the set S = {x € R" : ABx = 0} is a subspace of R".

Q: If V is any three-dimensional subspace of R°, then V has infinitely many bases.

Q: (2) Find a basis for the subspace W%3D { (а+c, 2a — b, За — 2b — с, b + 2с) | а, b, с € R} of R4.

Q: Let Mnn be a vector space of n x n matrices. Which of the following is not a subspace of Mnn?

A: The vector space of nxn matrix is Mnn.

Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2- )x²; a,b e R} of P,

Q: Determine if the set H of all matrices of the form is a subspace of M Here, p, q and 22 r represent…

Q: Determine whether the following are subspaces of R2×2: The set of all symmetric 2 × 2 matrices

Q: x1 + x2 + x3 = 0 x4+x₂+2x3 = 0

Q: If V = M2x2(R) and W consists of those elements of V in which at least one entry of the matrix is…

A: That's easy. Have a great day!!!

Q: Let A be an m×n matrix. Find all b such that the set of solutions to Ax = b is a subspace and prove.

A: Given: Let A be an m×n matrix. The objective is to find that the set of solutions to Ax =b is a…

Q: Find a basis and the dimensi on of the subspace W of V = M22 spanned by A B

A: V=M2X2R SPANNED BY A=1-5-42, B=11-15, C=2-4-57, D=1-7-51 Solution:- To find: A basis and the…

Q: In each part, find a basis for the given subspace of R, and state its dimension. a) All vectors of…

Q: Determine whether W is a subspace of V , V = Mnn, W is the set of idempotent n X n matrices

A: Let V be a vector space and let W be a nonempty subset of V. Then W is a sub-space of V if and only…

Q: Find a basis for W, the orthogonal complement of W, if W is the subspace spanned by 2

Q: 2. Determine if the set of all 2 x 2 matrices where tr(A) = 0 is a subspace of the vector space,…

Q: Find a basis for the subspace of R° consisting of all vectors perpendicular to v, that is find a…

Q: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

solve

Determine whether the set of all matrices of the form
b c
where a +c = 0, and b+ d + f = 0,
d e
is a subspace of the vector space M2x3, of all 2 x 3 matrices.

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 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

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

Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
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
In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In each case either prove that S forms a subspace of 2 or give a counterexample to show that it does not. xy0
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?
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=3, W={[aba]}