A square matrix A is idempotent if A² = A. t V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 × 2 empotent matrices with real entries. 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] 5 6 [[1,2], [3,4]], [[5,6],[7,8]] for the answer (Hint: to show that H is not closed under addition, it is sufficient to find two idempotent matrices A and B such that (A + B)² + (A + B).) 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 [3 4 as 2, [[3,4],[5,6]] for the answer 2, (Hint: to show that H is not closed 5 6 under scalar multiplication, it is sufficient to find a real number and an idempotent matrix A such that (rA)² + (rA).) 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: A square matrix A is idempotent if A² = A. Let V be the vector space of all 2 x 2 matrices with real…

A:

Q: The trace of a square n x n matrix A = (a,j) is the sum a11+ a22 + entries on its main diagonal.…

A: Subspace of the vector space

Q: Determine whether the set of all 3×3 diagonal matrices with the standard operations, is a vector…

A:

Q: Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector…

A: The given set is a11b | a, b∈K. It is known that any subspace should contain the identity element.

Q: 16х 4y 4z -4 4x 10y 4z 4x 4y 6z -2 %3D -4х 2y -2z 4 I| || || ||

A: The solution is given as

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

A: The given question is solved below.

Q: A square matrix A is idempotent if A² A. Let V be the vector space of all 2 × 2 matrices with real…

A:

Q: Let S be the set of matrices of the form a -a :). -b b where a and be R. The vector addition and…

A:

Q: Let V be the set of all (6x6) real skew-symmetric matrices. It can be shown that V is a vector space…

A: Given : V be the set of all (6x6) real skew-symmetric matrics

Q: lp with calculus

A: Given,

Q: The trace of a square 1 x n matrix A = (a) is the sum a1 + a22+...+ of the entries on its main…

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: A square matrix A is nilpotent if A" = 0 for some positive integer n. == Let V be the vector space…

A: 1. Yes H contains the zero vector2. No. H is not closed under addition. 3. Yes, H is closed under…

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: Let V be the set of all (4x4) real skew-symmetric matrices. It can be shown that V is a vector space…

A:

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

A:

Q: Let W be the set of all 2 x 2 symmetric matrices. Show that. W is a subspace of M2x2(R). Recall that…

A:

Q: Let A,B ∈ Matn(F ) denote two square matrices. Assume that A and B are row equivalent. Show that B…

A: The objective of this question is to prove that if two square matrices A and B are row equivalent,…

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

A: Solution:-

Q: There exists a 3 x 3 orthogonal matrix A such that 2 A 0 = True False

A:

Q: Determine if the vector u is in the column space of matrix A and whether it is in the null space of…

A:

Q: A square matrix A is nilpotent if A"= 0 for some positive integer n. Let V be the vector space of…

A:

Q: What is the dimension of the column space of A? What is the dimension of the null space of A? What…

A: In this question, we have given  A be a 13×19 matrix with rank=11 we need to find the followings:…

Q: Find a redundant column vector of the given matrix A, and write it as a linear combination of…

A:

Q: Let T(x) = Ax for the matrix A and [4 -4 -16] -16, b = A = 7 5 Lo 0 1 1 Select true or false for…

A: Given that  A=4-4-1675-16011, b=3-11, c=-451 Select true or false statement.

Q: Suppose there exists a 2x2 diagonal matrix with a standard operation. Prove that this set is a…

A: