The trace of a square n x n matrix A = (aj) is the sum a₁1 + a22 + ... +ann of the entries on its main diagonal. Let V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 x 2 matrices with real entries that have trace 0. Is H a subspace of the vector space V? 1. Is H nonempty? choose 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in H whose sum is not in H, using a comma separated list and syntax such as [[1,2],[3,4]], [[5,6],[7,8]] for the answer 1 5 6 3 (Hint: to show that H is not closed under addition, it is sufficient to find two trace zero 4 matrices A and B such that A + B has nonzero trace.) 8 3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a matrix in H whose product is not in H, using a comma separated list and syntax such as 2, [[3,4],[5,6]] for the ·[31]. (Hint: to show that H is not closed under scalar multiplication, it is sufficient to find a 6 real number and a trace zero matrix A such that rA has nonzero trace.) answer 2, 4. Is H a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3. choose

Q: If you are given a matrix M such that M = [p 4 5 q 5 4  r 0 5] , define the vector [p q r]…

A:

Q: 20 5 -1 6 2 The null space for the matrix 4 4 -1 5 4 1 0 11 is spanned by the vector 10

A: Definition of Null Space of a Matrix The null space of an m × n matrix A is the set of all the…

Q: Let A and B be 2x2 matrices such that B is invertible If detA)2 and det)-, then detA'e) Select one:…

A:

Q: Find the null space of the following matrix: A= [( 1,0,2,),(0,1,1),(0,0,0),(0,0,0)]

A:

Q: Find a non-zero vector in Nul A and a non-zero vector in Col A for the following matrix: 1 2 4 5 -5…

A:

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: Let A = and B = {b1.b2.b3} be bases for a vector space V, and suppose a, = 5b, - b2, az = - b, + b2…

A: Bases of a vector space

Q: Let X be an n-dimensional random vector and the random vector Y be defined as Y = AX + b, where A…

A: It is widely used in statistics . It has applications in almost all multivariate problems .

Q: Please go through each option with explanation

A:

Q: Find a basis for the subspace of Mnxn consisting of all diagonal matrices.

A:

Q: .

A: A vector is given X=x1x2⋮xn which can be viewed as an n×1 matrix X. (a) We have to compare Matrix…

Q: Find an SVD of the indicated matrix. (Enter each matrix in the form [[row 1], [row 2], ...], where…

A:

Q: Determine if the column space of the matrix A included contains the vector(11,−9,5,7). If so,…

A: Given below the detailed solution.

Q: Find a basis, and the dimension, of the vector space of all matrices of order 3.

A:

Q: Exhibit a basis for M2x2, the vector space of all 2 x 2 matrices of real numbers.

A:

Q: Let W be the set of all vectors C2 C3 CA such that 1-2x2 = 423 and 2x1 = 3 + 3x4 Determine if W is a…

A: Given that W has vectors of form               We have to check that W form a vector space or not…

Q: Let A be an n × n matrix and {v1, v2,..., vk } a linearly dependent set of vectors in Rn. Are Av1,…

A: Linear dependent: A finite non empty set of vectors v1, v2, ...vkis said to be linear dependent if…

Q: d) If A and B are 4 x 4 nonsingular matrices such that |2A¬'B²| = 32, then |4| = 8 e) Let S =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let W be the set of all vectors of the form [3s 4r5t] 2r + 2s - t 3s - r + 5t 3r + 2s + 4t with r, s…

A: The set ( W ) consists of vectors that can be formed by linear combinations of the vectors with…

Q: -9 -10 12 -15 A = 4 -8 6 6 0 9

A:

Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = [0.375,…

A: Given Data: The given details are We want to create a matrix that reflects around a line that is…

Q: Let A be an m x n matrix and let b be a vector of length n. If A x = b is consistent then rank(A) =…

A: We can check whether the given statement is true or false.

Q: Let M be the vector space of 2 x 2 real-valued matrices. For M = [ a b c d] we define M# = [d b…

A:

Q: Find an explicit description of the null space of matrix A by listing vectors that span the null…

A:

Q: Find vectors that span the null space of the following matrices. [1 3 -4 -3 1 1 2 2 4 0 b. 0 1 -3 1…

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

Q: Find an explicit description of the null space of the given matrix by listing vectors that span the…

A:

Q: e a square Fits diagona diagonal ele anal the val

A:

Q: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

A: Solution:-

Q: Consider the vector space PA(R) = {ax + bæ³ + ca? + dx + e : a, b, c, d, e E R} of polynomials of…

A: Note:- for this problem you don't mention about f1, f2, f3 (should i have to take  f1, f2, f3…

Q: Let A = {a,,a2,a3} and B = (b1,b2.b3} be bases for a vector space V, and suppose a, = 4b, - b2, a2 =…

A: Given that A=a1,a2,a3 and B=b1,b2,b3 be bases for a vector space V, and given…

Q: Let V₁ = (1,4,5,6,9), v₂ =(3, 2, 1,4, -1), V3 = (-1,0,-1, -2, -1), V4=(2,3,5,7,8), Find a basis for…

A:

Q: 2- Let v toe with real entries · Then Check Ų formes ailo Vector space or not the set of all 2x2…

A: