Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form [88] V = M₂,2 Wis a subspace of V. Ow is not a subspace of V because it is not closed under addition. OW is not a subspace of V because it is not closed under scalar multiplication.

Q: Determine whether W = {a + 2x + bx²|a, b = R} is a subspace of P2.

A: Explanation of the answer is as follows

Q: a) Is A diagonalizable? Explain. b) If A is diagonalizable, rewrite A as XDX-1 (explain the choice…

A: a) Given            A=310010-310

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: Let V be the vector space of all (3×3) matrices and W be the set of all (3×3) matrices A for which…

A:

Q: Prove that the n × n identity matrix is orthogonal.

A:

Q: Algbra prove that A is invertible if AT(a transpose)+A is a positive definite matrix.

A: Given that If A^T+A is a positive definite matrix For a positive definite matrix Det(A^T+A)>0. So…

Q: X = 4 1 -3 0 0 6 1 2 -12 10 -1 = [X₁ 5 X2 X3 X4]

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: Let ¹ = [ 8 ], x= [ ¦ ! ] x = [ 9 ] -[69]-[88]-[8][9] Show that these four matrices span M2(C), the…

A:

Q: Determine the dimensions of Nul A and Col A for the matrices. A = 10

A:

Q: 20) Let W be the vector space of all symmetric 2 x 2 matrices. Show that W sisomorphic to R³

A: Introduction: The set of vectors v1, v2, ..., vn in V is said to be linearly independent if the only…

Q: Suppose A is invertible.  Explain AT A is invertible.

A: The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the…

Q: Construct a 3 x 3 matrix A with nonzero entries, and a vector b in R³ such that b is not in the set…

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 and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: Does the set of all 2x2 matrices form a vector space, please explain.

A:

Q: X = 4 0 1 0 -3 6 1 2 -12 10 -1 = [X₁ X₂ X3 X4] 5

A: Linear algebra

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

A:

Q: Q4 let V=M₂x₂ of the form [a of with standard matrix addition and multiplication form -space-

A:

Q: Determine the dimensions of Nul A and Col A for the matrices. A =

A:

Q: Let V = M² X 2 (R) be the vector space of all real 2 x 2 matrices. Determine if the following…

A: