Answered: 6. The set of all 2 × 2 matrices of the…

6. The set of all 2 × 2 matrices of the form a. is a vector space. b. is not a vector space because addition is not commutative. c. is not a vector space because it is not closed under addition.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.

See similar textbooks

Related questions

Q: Let V denote the set of all 1×3 matrices over R, and define usual addition on V as for M1×3. If the…

Q: Show that Rm×n, together with the usual addition and scalar multiplication of matrices, satisfies…

Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subepace w - q W- span Find a…

A: First we calculate the basis of V.

Q: Let M,xn be a set of squarenx n-matrices. Is the set Mnxn a vector space? Explain. Find 2 different…

A: We find two different basis of M_2×2

Q: The set V being the space of matrices of type form a : a, b,c, d e R 2x2 vector space according to…

A: Given set V=abcd: a,b,c,d∈R.

Q: The set of all 2x3 matrices with the standard operations is a vector space. Select one: O True O…

A: 1.The set of all 2×3 matrices with the standard operations is a vector space.2.The null space of a…

Q: 6: Let V be the vector space of all symmetricnx n matrices over R. Then dimension of V is n(n - 1)…

A: Please refer to the below-uploaded images to step by step solution to your problem.

Q: 3. Consider the following matrices: 9. A = 6 2 A2 14 0 A3 = A4 = As = %3D 27 3 Find the dimension of…

A: given system of equation A1=94273 , A2=62140 , A3=1958 , A4=301-3 , A5=2785 claim- find the…

Q: Write down the standard basis for each of the following vector spaces. (a) R3 (b) Р, (c) M22

Q: Consider the set of all 3x3 matrices. Prove that with standard addition and standard multiplication…

A: The given question is solved below.

Q: Show that if S is a basis for a vector space V then every vector in V can be written in one and only…

Q: (a) Prove that if A and B are similar n x 11 matrices, then tr(A) = tr(B). (b ) How would you…

A: We are given two matrices A and B and they are similar. We are asked to proved tr(A)=tr(B). Next we…

Q: 1. The following is a list of sets with operations of addition and scalar multiplication defined on…

Q: 8) Determine whether B is a basis for the indicated vector space. a) B- {(6, -5), (12, -10)} for R

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the dimensions of the following vector spaces a) The space of all 5 x 5 diagonal matrices (b)…

A: Solution: a) The dimension is 5. There are 5 entries of diagonal 5 by 5 matrices.

Q: 4. Let A be an m x n matrix and b a non-zero m × 1 matrix. Show that the set of all n x 1 (column)…

Q: IfV is an n dimensional vector space, then any n linearly independent set of vectors in V is a basis…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Determine whether S is a basis for the given vector space.S = {(4, −3), (5, 2)} for R2

Q: 14 - Which one is a basis for the vector space R3 ? 1

A: We have to check

Q: Determine whether the set B is a basis for the space V. (a) B = {x² + x + 1, x² + 2, x + 3} and V is…

A: Definition of basis:- A set is said to be basis if it satisfy the following property (i) Set is…

Q: 5. Let a b c d M2,2 | a, b, c, d E R Show that M22 with the usual matrix addition and scalar…

Q: Prove that the set S of all matrices in M22 that have zeroes in exactly 2 entries spans M22. (Hint:…

Q: Let V be the set of 2 × 2 matrices with entries from R, that is, V ={ [ a b c d ] | a, b, c, d ∈ R }…

Q: 5. Let a b M22 | а, b, с, d € R с d Show that M22 with the usual matrix addition and scalar…

Q: Let A and B be similar nxn matrices. Prove that if A is idempotent, then B is idempotent. (X is…

A: According to the given information, it Let A and B be n×n similar matrices. If A is idempotent the…

Q: C along with the following operations defined: (a1, a2) + (b1, b2) =(a1 +b1 + 1, az + b2 +1) C •…

Q: 1. Suppose that V is a vector space and H is a subspace of V and the vectors vl,v2,...,vj all belong…

A: We have given that V is a vector space and H is a subspace of V, so H is also a vector space . Now…

Q: SHOW THAT THE SET OF TYPE MATRICES "mxn" IS A VECTOR SPACE OF MATRICES TYPE "mxn" (M(mxn) [R], +, .)

A: To check all the axioms of a vector space and to determine whether it is a vector space or not.

Q: linear algebra

A: To show every 2 by 2 matrix is a linear comination of the 4 gicen matrices. Also , to determine four…

Q: Show that each of these is not a vector space. (Hint. Start by listing two members of each set.) 1.…

Q: Show that the following is NOT a (real) vector space: the set of all 2 ×2 matrices, with the usual…

Q: 6. The set of all 2 x 2 matrices of the form a. is a vector space. b. is not a vector space because…

A: The solution are next step ...

Q: 7. Suppose A Matnxn (F) is a matrix with det(A) #0. Prove that Espan{Id, A, A²,..., An-1}. A

Q: The set of m x n matrices is not a vector space under matrix addition and scalar multiplication.…

Q: Which of the following is not a vector space? (; :) A. The set of all 2x2 matrices of the form with…

A: Solution:-

Q: Let u be a vector in R" and A be an m × n matrix. If u is orthogonal to each row of A then u is in…

A: Since u is orthogonal to each row of A, it means u is in null space of A.

Q: 1. The following is a list of sets with operations of addition and scalar multiplication defined on…

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

Q: Determine whether S is a basis for the given vector space.S = {(1, 5, 3), (0, 1, 2), (0, 0, 6)} for…

Q: 4. Let Mag, denote the set of all n x n magic squares, and let Mag, denote the set of all n xn magic…

Q: linear algebra

A: To show that any square matrix of order 2 (2 x 2) is a linearl combination of the four given…

Q: The set of all 2x2 symmetric matrices is a vector space Select one: O True O False

A: Note the result : V :Set of all 2×2 matrices is a vector space over ℝ . A : Set of all symmetric…

Q: Show that each of these is not a vector space. (Hint. Start by listing two members of each set.) 1.…

A: 1. Let a=100 and b=1-11 belong to given set. Then, a+b=1+0+0+1-1+1=2 Therefore, a+b does not belong…

Q: Determine whether the given set, together with the specified operations of addition and scalar…

A: We are to determine whether the given set, together with the specified operations of addition and…

Q: 3. Give any element belongs to the vector space C³(-00,00)

A: Given vector space is C3-∞,∞ or C3R where R=-∞,∞ set of real numbers.

Q: 3. Show that if two vectors in the set {a1, a2,... , ak} are identical, then the set is linearly…

Q: 6. The set of all 2 x 2 matrices of the form " 1 a. is a vector space. b. is not a vector space…

Q: 1. Consider the set of all 3x3 matrices. Prove that with standard addition and standard…

Q: (e) The set of normal matrices is closed under unitary conjugation.

A: To show: The set of normal matrices is closed under unitary conjugation.

Question

matrix

6. The set of all 2 x 2 matrices of the form : 1
a. is a vector space.
b. is not a vector space because addition is not commutative.
c. is not a vector space because it is not closed under addition.

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 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Markov Processes and Markov chain$

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

Prove that if A is similar to B and A is diagonalizable, then B is diagonalizable.
Prove that in a given vector space V, the additive inverse of a vector is unique.
Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
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.
Prove that in a given vector space V, the zero vector is unique.
For each of the following matrices A in SL(2,R), list the elements of A and give the order | A |. a. A=[ 0111 ] b. A=[ 1110 ]
Identify the zero element and standard basis for each of the isomorphic vector spaces in Example 12. EXAMPLE 12 Isomorphic Vector spaces The vector spaces below are isomorphic to each other. a. R4=4space b. M4,1=spaceofall41matrices c. M2,2=spaceofall22matrices d. P3=spaceofallpolynomialsofdegree3orless e. V={(x1,x2,x3,x4,0):xiisarealnumber} subspace of R5